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Annabel wants to make banana bread for the bake sale. She went to the market to buy bananas, and she noticed fruit flies after she returned home with her produce. The number of fruit flies grows at an exponential rate modeled by the equation f(t)=8(2)t

, where f is the number of fruit flies after t days. Define an appropriate domain for the problem if Annabel bakes the banana bread 5 days after returning from the market.(1 point)
Responses

0≤t≤256
0 less than or equal to t less than or equal to 256

0≤f≤256
0 less than or equal to f less than or equal to 256

0≤f≤5
0 less than or equal to f less than or equal to 5

0≤t≤5
0 less than or equal to t less than or equal to 5

Callie entered an art contest in second grade and won a $1,000 scholarship. The money was invested in an account paying a 9% interest rate compounded annually. The situation can be modeled by the equation a(t)=1,000(1.09)t
, where a is the amount in the account after t years. If Callie uses the scholarship 10 years later, determine which graph accurately displays the situation.(1 point)
Responses

An increasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 2,000 in increments of 500.
Image with alt text: An increasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 2,000 in increments of 500.

An increasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 5 in increments of 1 and the y-axis ranges from 0 to 2000 in increments of 500.
Image with alt text: An increasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 5 in increments of 1 and the y-axis ranges from 0 to 2000 in increments of 500.

An increasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 14 in increments of 2 and the y-axis ranges from 0 to 3,500 in increments of 500.
Image with alt text: An increasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 14 in increments of 2 and the y-axis ranges from 0 to 3,500 in increments of 500.

A decreasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 12 in increments of 2 and the y-axis ranges from 0 to 1,200 in increments of 200.

Use the table to answer the question.

0 350
1
2
3
4
5 A certain population of beetles is increasing at a rate of 22% per month. If there are currently 350 beetles, the equation f(x)=350(1.22)x
can be used to model the situation. Finish the chart and plot the points to determine which graph correctly displays the situation.(1 point)
Responses

An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
Image with alt text: A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.

A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
Image with alt text: A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.

An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 2,000 in increments of 200. The y-axis for Beetles ranges from 0 to 10 in increments of 1.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 2,000 in increments of 200. The y-axis for Beetles ranges from 0 to 10 in increments of 1.

Use the image to answer the question.

A decreasing curve with an arrow on the end is plotted on a coordinate plane. The curve begins at the point left parenthesis 0 comma 700 right parenthesis.

The value of a cell phone decreases exponentially at a rate of 24% each year after its release date. If the initial value of the phone is $700, the situation can be modeled by the equation v(t)=700(0.76)t
, where v is the value of the cell phone t years since its release date. Interpret the graph of the equation and identify the true statement.

(1 point)
Responses

As t increases, v increases slowly at first and then quickly.
As t increases, v increases slowly at first and then quickly.

As t increases, v decreases slowly at first and then quickly.
As t increases, v decreases slowly at first and then quickly.

As t increases, v decreases quickly at first and then slowly.

Use the image to answer the question.

An increasing curve with an arrow on the upper end is plotted on a coordinate plane. The x-axis is labeled people and ranges from 0 to 5 in increments of 1. The y-axis is labeled money and ranges from 0 to 500 in increments of 100.

Mason is completing a study for his psychology course. For the study, he begins with $20 and asks individuals on the street if they want the money or if they would like him to double it and give it to the next person. He continues to do this until someone takes the money. This situation can be modeled by the exponential equation m(p)=20(2)p
, where m is the money and p is the number of people who opt to pass it on to the next person. Which of the following statements is true about the equation?

(1 point)
Responses

As p increases, m decreases slowly at first and then quickly.
As p increases, m decreases slowly at first and then quickly.

The domain (p-values) include the values greater than or equal to 20 (p≥20)
.
The domain ( p -values) include the values greater than or equal to 20 left parenthesis p greater than or equal to 20 right parenthesis .

As p increases, m increases quickly at first and then slowly.
As p increases, m increases quickly at first and then slowly.

The range (m-values) includes the values (m≥20)
.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
yesterday

Let’s address each question one by one:

  1. Domain for fruit flies: The equation \( f(t) = 8(2)^t \) models the number of fruit flies after \( t \) days, and Annabel bakes the banana bread 5 days after returning from the market. The appropriate domain would be the range of time from when she gets the bananas (t = 0) until she bakes the bread (t = 5), therefore:

    Answer: \( 0 \leq t \leq 5 \) (or \( 0 \leq t \leq 5 \)).

  2. Graph for Callie's scholarship: For the equation \( a(t) = 1000(1.09)^t \), after 10 years, the amount in the account will be computed using the model. The graph should correctly show an increasing curve over the span of 10 years.

    The graph that fits this is: Answer: An increasing curve with an arrow at the end is plotted in the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 2,000 in increments of 500.

  3. Population of beetles: For the equation \( f(x) = 350(1.22)^x \), starting with 350 beetles, we need to fill out the table:

    • For \( x = 0 \): \( f(0) = 350(1.22)^0 = 350 \)
    • For \( x = 1 \): \( f(1) = 350(1.22)^1 = 427 \) (approximately)
    • For \( x = 2 \): \( f(2) = 350(1.22)^2 \approx 520 \) (approximately)
    • For \( x = 3 \): \( f(3) = 350(1.22)^3 \approx 634 \) (approximately)
    • For \( x = 4 \): \( f(4) = 350(1.22)^4 \approx 774 \) (approximately)
    • For \( x = 5 \): \( f(5) = 350(1.22)^5 \approx 944 \) (approximately)

    This shows the population increases over the months. An increasing curve graph would accurately reflect this.

    Answer: An increasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.

  4. Value of a cell phone: The equation \( v(t) = 700(0.76)^t \) models the decreasing value of the cell phone over time. Since the equation decreases exponentially, the true statement should reflect that.

    Answer: As t increases, v decreases slowly at first and then quickly.

  5. Money doubling situation: The situation modeled by \( m(p) = 20(2)^p \) grows exponentially as people are asked to double the money. The statement that corresponds to this growth should indicate that as \( p \) increases, the amount of money increases significantly.

    Answer: As p increases, m increases quickly at first and then slowly.

Feel free to ask if you need further clarification on any of these points!