Quiz about Equivalent Exponential Expressions

Question 1

An investment in a particular retirement account triples every 12 years. The expression $$5000\left(3\right)^{\frac{t}{12}}$$ represents the amount in the account, in dollars, t years after the account is open. Which statement is true?

Accepted Answer

The expression $$5000\left(1.096\right)^t$$ is approximately equivalent which shows a growth rate of 9.6% per year.

Answer

The expression $$5000\left(1.096\right)^t$$ is approximately equivalent which shows a growth rate of 96% per year.

Answer

The expression $$5000\left(0.25\right)^t$$ is approximately equivalent which shows a growth rate of 25% per year.

Answer

The expression $$5000\left(0.25\right)^t$$ is approximately equivalent which shows a growth rate of 0.25% per year.

Question 2

Select two expressions equivalent to $$16\left(2\right)^{n-3}$$

Accepted Answer

$$\left(2\right)^{n+1}$$

Accepted Answer

$$8\left(2\right)^{n-2}$$

Answer

$$\left(2\right)^{4n-12}$$

Answer

$$\left(2\right)^{4n-3}$$

Answer

$$8\left(2\right)^{n-1}$$

Question 3

Select two expressions equivalent to $$27\left(3\right)^{n-3}$$

Accepted Answer

$$\left(3\right)^n$$

Accepted Answer

$$3\left(3\right)^{n-1}$$

Answer

$$9\left(3\right)^{n+1}$$

Answer

$$9\left(3\right)^{3n-1}$$

Answer

$$\left(3\right)^{3n-3}$$

Question 4

The population of pigeons in a city can be represented by the following expression $$230\left(1.18\right)^t$$ . Which expression below represents the population of pigeons after t years where the quarterly rate can be found? What is the quarterly rate?

Accepted Answer

$$230\left(1.0422\right)^{4t};$$ $$\ r=4.22\%$$

Answer

$$230\left(1.18\right)^{4t};$$ $$\ r=0.18\%$$

Answer

$$230\left(1.18\right)^{4t;}$$ $$\ r=118\%$$

Answer

$$230\left(1.0422\right)^{4t};$$ $$r=104.22\%$$

Question 5

The value of an antique car is modeled by the function $$v\left(t\right)=107,000\left(1.125\right)^t$$ , where t is the number of years since 2005. Which equation can be used to find the quarterly rate?

Accepted Answer

$$V\left(t\right)=107,000\left(1.0299\right)^{4t}$$

Answer

$$V\left(t\right)=107,000\left(1.0299\right)^t$$

Answer

$$V\left(t\right)=107,000\left(1.125\right)^{4t}$$

Answer

$$V\left(t\right)=107,000\left(1.125\right)^{\frac{1}{4}t}$$

Question 6

The value of a brand new car is $42,000 and the value depreciates 23% per year. What would the quarterly rate of change be to the nearest hundredth of a percent?

Accepted Answer

6.33%

Answer

0.63%

Answer

0.77%

Answer

0.9367%

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