Question 1 A) Drag and drop the expressions into the correct locations. Perry buys a bag of 20 carrots on the first day. The second day, he eats half of the bag. Each day after, he eats half of what is left in the bag. Create a sequence formula that describes the number of carrots Perry will have on any given day. (1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. an=an=Coefficient of the sequence formula is ⋅⋅ Exponential factor of the sequence formula is 20(12)n−1(12)n−12(120)n−1(120)n−1 Question 2 A) The equation y=4,060(1−0.05)ty=4,060(1−0.05)t represents the decay of a specific species of bird. Select the option below that represents the rate of decay for the species. Option #1: The rate of decay is 0.05%. Option #2: The rate of decay is 203. Option #3: The rate of decay is 5%. (1 point) Option #$$ in the correct rate of decay. Question 3 A)In a certain geographic location, a herd of antelopes is declining at a rate of six percent every year. If there are currently 570 antelopes in the herd, create an exponential decay function to model the problem. If the decrease in population continues at this rate, how many antelopes will be in the herd after 10 years? Round your answer to the nearest whole number.(1 point) After 10 years there will be $$ antelopes. Question 4 A) Use the image to answer the question. Use the graph of the exponential decay function to determine the equation for the horizontal asymptote of the sequence that is modeled by the graph. (1 point) The horizontal asymptote is at y=y=$$. Question 5 A)Using the discussed properties of exponential decay graphs, find the y-intercept of the function y=30(0.85)xy=30(0.85)x that models an exponential sequence.(1 point) The y-intercept is at the point (0,$$).

Question

question 4 graph: point:(0,3)
second point:y=3(0.75)^x

Answer 1

Sure! Here are the answers to the questions based on the information provided:

Question 1

Perry's sequence formula regarding the number of carrots is:

• Coefficient of the sequence formula is 20.
• Exponential factor of the sequence formula is (1/2)^(n-1).

Question 2

The equation \( y=4,060(1−0.05)^t \) represents the decay of a specific species of bird. The rate of decay is:

• Option #3: The rate of decay is 5%.

Question 3

To create an exponential decay function for the antelope population, we use the formula:

\[ P(t) = P_0 (1 - r)^t \]

Where:

• \( P_0 = 570 \) (initial population)
• \( r = 0.06 \) (rate of decline)
• \( t = 10 \) (years)

So the function becomes:

\[ P(t) = 570 (1 - 0.06)^{10} = 570 (0.94)^{10} \]

Calculating this gives:

\[ P(10) \approx 570 \times 0.537 \approx 306.09 \]

Rounding to the nearest whole number, there will be 306 antelopes after 10 years.

Question 4

Based on the graph modeled by the points and the equation \( y = 3(0.75)^x \), the horizontal asymptote can be derived. The horizontal asymptote approaches \( y = 0 \) as \( x \) increases, but considering the graph's behavior at lower values:

• The horizontal asymptote is at y = 0.

Question 5

For the function \( y = 30(0.85)^x \), to find the y-intercept, we set \( x = 0 \):

\[ y = 30(0.85)^0 = 30(1) = 30 \]

So the y-intercept is at the point (0, 30).

In summary:

• After 10 years, there will be 306 antelopes.
• The horizontal asymptote is at y = 0.
• The y-intercept is at the point (0, 30).