Ask a New Question
Menu

Which of the following situations could describe the graph?

(1 point)
Responses

Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.
Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

There are 200 cockroaches in a building, and the population triples every day.
There are 200 cockroaches in a building, and the population triples every day.

Niall rents a bike for $20 per hour.
Niall rents a bike for $20 per hour.

Juveldy puts $20 in a high-yield savings account. His investment triples every year.

11 answers

To determine which situation could describe the graph, we need to analyze the scenarios:

  1. Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

    • This is an example of exponential growth (specifically, a percentage increase of the current value). The value can be modeled as \( V(t) = 20 \times (1.2)^t \).

  2. There are 200 cockroaches in a building, and the population triples every day.

    • This is also an example of exponential growth, with a model of \( P(t) = 200 \times (3)^t \), where \( t \) is in days.

  3. Niall rents a bike for $20 per hour.

    • This situation represents a linear relationship, where the cost increases linearly with time. The model would be \( C(t) = 20t \), where \( t \) is in hours.

  4. Juveldy puts $20 in a high-yield savings account. His investment triples every year.

    • This is another example of exponential growth and can be modeled as \( I(t) = 20 \times (3)^t \).

The first, second, and fourth options represent exponential growth, while the third represents linear growth. Without seeing the specific graph, we can conclude that:

  • If the graph depicts exponential growth, it could represent any of the first, second, or fourth situations.
  • If it depicts linear growth, then it would correspond to the third situation.

So, depending on the nature of the graph, options 1, 2, and 4 depict exponential growth, while option 3 represents a linear relationship. If you provide the graph characteristics, I can help identify the most likely match.

just the answer

Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

Lori buys five goldfish for her tank. Her research shows that they will reproduce at a rate of 32 percent each month. Which statement discusses a key feature of the graph of this situation?(1 point)
Responses

The graph will begin with the point (1,5)
because Lori starts with five fish.
The graph will begin with the point left parenthesis 1 comma 5 right parenthesis because Lori starts with five fish.

The graph will have a constant rate of change.
The graph will have a constant rate of change.

The points on the graph will have a common ratio of 1.32.
The points on the graph will have a common ratio of 1.32.

The points on the graph will have a common ratio of 32.

The correct statement is:

The points on the graph will have a common ratio of 1.32.

What is the initial value of the sequence?

(1 point)
Responses

1
1

0.5
0.5

0
0

2

The correct answer for the initial value of the sequence is 1.

A local bakery opened with new equipment worth $80,000. Ten years later, the owners’ accountants told them that their equipment had depreciated at a rate of 6 percent per year. Which equation would you use to create a sequence modeling this situation?(1 point)
Responses

an=80,000(0.06)n
a subscript n baseline equals 80,000 left parenthesis 0.06 right parenthesis superscript n baseline

an=80,000(0.06)n−1
a subscript n baseline equals 80,000 left parenthesis 0.06 right parenthesis superscript n minus 1 baseline

an=80,000(0.94)n
a subscript n baseline equals 80,000 left parenthesis 0.94 right parenthesis superscript n baseline

an=80,000(0.94)n−1

The correct equation to model the depreciation of the equipment is:

\( a_n = 80,000(0.94)^n \)

This equation reflects a yearly depreciation of 6%, which means the value of the equipment retains 94% (100% - 6%) of its value each year.

In a certain geographic location, a herd of elephants is declining at a rate of four percent every year. If there are currently 62 elephants in the herd, create an exponential decay function to model the problem. Let y represent the number of elephants after t years.(1 point)
Responses

y=62(1.04)t
y equals 62 left parenthesis 1.04 right parenthesis superscript t baseline

y=62(0.6)t
y equals 62 left parenthesis 0.6 right parenthesis superscript t baseline

y=62(0.04)t
y equals 62 left parenthesis 0.04 right parenthesis superscript t baseline

y=62(0.96)t

The correct exponential decay function to model the decline of the elephant herd is:

\( y = 62(0.96)^t \)

This reflects a decline of 4% per year, meaning the herd retains 96% of its population each year (100% - 4% = 96%).