Quiz about Exponential Models

Question 1

After the last ice age began, the number of plant species in South America changed rapidly.

The relationship between the elapsed time, $${t}$$, in years, since the ice age began, and the total number of plant species, $${P}({t})$$, is modeled by the following function: $$P(t)=30,000,000$$. $$(\frac{8}{9})^{t}$$

Complete the following sentence about the yearly rate of change of the number of plant species.

Every year, the number of plant species shrinks by a factor of $$ \ldots \ldots $$

Accepted Answer

Covalent bond

Answer

$$\frac{8}{9}$$

Answer

$$0.8$$

Answer

$$1$$

Answer

$$30,000000$$

Question 2

The population of snails in a tank at the aquarium is found to triple every year. Mark visits the aquarium and counts 80 snails in the tank.

Write a function $$f(n)$$ to model the number of snails in the tank $$n$$ years after Mark's visit.

Accepted Answer

Covalent bond

Answer

$$f(n)=80.2^{n}$$

Answer

$$ f(n)=80.3^{n}$$

Answer

$$f(n)=80 . f(1)$$

Answer

$$f(n)=40.2^{n}$$

Question 3

The table shows the value in dollars of a motorcycle at the end of $x$ years.
![](http://admin.getprephub.com/media/editor/Screenshot%202023-05-29%20at%205.03.15%20PM_20230529150326500690.png)
Which exponential function models this situation?

Accepted Answer

Covalent bond

Answer

$$ v(x)=9000(0.9)^x $$

Answer

$$ v(x)=9,000(1.1)^x $$

Answer

$$ v(x)=8,100(1.1)^x $$

Answer

$$ v(x)=8,100(0.9)^x $$

Question 4

On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The locust population increases by a factor of 5 every 22 days, and can be modeled by a function, $${L}$$, which depends on the amount of time, $${t}$$ (in days).

Before the first day of spring, there were 7600 locusts in the population.

Write a function that models the locust population $$t$$ days since the first day of spring.

Accepted Answer

Covalent bond

Answer

$$L(t)=7600(5)^{\frac{t}{22}}$$

Answer

$$L(t)=7600(5)^{22 t}$$

Answer

$$L(t)=7600(1+\frac{5}{100})^{t}$$

Answer

$$L(t)=7600(1-\frac{5}{10}.$$

Question 5

Nora uploaded a funny video on her website, which rapidly gains views over time.

The relationship between the elapsed time, $${t}$$, in days, since Nora uploaded the video, and the total number of views, $${V}({t})$$, is modeled by the following function: $$V(t)=100 \cdot(1.53)^{t}$$

Complete the following sentence about the daily rate of change in the views of the video.

Every day, the number of views by a factor of $$\ldots \ldots$$

Accepted Answer

Covalent bond

Answer

$$1.53$$

Answer

$$53$$

Answer

$$100$$

Answer

$$t$$

Exponential Models Algebra 2 Maths Problems and Solutions

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