Quiz about Real World Exponential Equations

Question 1

Halle deposited $4000 into an account that earns 5% interest each year. The growth of her investment can be expressed by the exponential equation, A = 4000(1 + .05)^t, where A is the amount in the account after t years. In how many years will her account exceed $10,000?

Accepted Answer

19 years

Answer

16 years

Answer

22 years

Answer

25 years

Question 2

The equation of an exponential function is given as follows: $$f\left(x\right)=100\left(1.2\right)^x$$ . What is the initial value of the function?

Accepted Answer

100

Answer

1.2

Answer

10

Answer

0.8

Question 3

The equation of an exponential function is given as follows: f(x)=100(1.2)^x . Does this equation represent exponential growth or decay and what is the exponential growth or decay rate?

Accepted Answer

Growth, 20%

Answer

Growth, 120%

Answer

Decay, 20%

Answer

Decay, 12%

Question 4

The equation of an exponential function is given as follows: f\left(x\right)=8\left(0.75\right)^x . Does this equation represent exponential growth or decay and what is the exponential growth or decay rate?

Accepted Answer

Decay, 25%

Answer

Growth, 75%

Answer

Growth, 25%

Answer

Decay, 75%

Question 5

A population of bacteria doubles every hour. If the initial population is 500, which function models the population after $$x$$ hours?

Accepted Answer

$$P(x)=500\left(2\right)^x$$

Answer

$$P(x)=2\left(500\right)^x$$

Answer

$$P(x)=2\left(500x\right)$$

Answer

$$P(x)=500+2^x$$

Question 6

The amount of downloads for an album on iTunes, g(d), where d is the number of days since the album was first uploaded can be represented as
g(d) = 5^1.5d
How many downloads will the album have after 3 days?

Accepted Answer

1398

Answer

125

Answer

11

Answer

140

Question 7

An experiment begins with 20 grams of a radioactive isotope. This isotope has a half-life. If y is the mass in grams remaining after x half-lives have elapsed, which equation represents the amount of grams the isotope will weigh after 4 half-lives?

Accepted Answer

$$y=20\left(\frac{1}{2}\right)^4$$

Answer

$$y=20\left(2\right)^4$$

Answer

$$y=4\left(20\right)^{\frac{1}{2}}$$

Answer

$$y=20\left(4\right)^{\frac{1}{2}}$$

Question 8

The population of wolves in an area is represented by the function $$y=800\left(0.95\right)^x$$ where x is the number of years since the year 2000.

How many wolves are there in 2011?

Accepted Answer

455 wolves

Answer

455.04007 wolves

Answer

no wolves

Answer

8360 wolves

Question 9

If a quantity doubles every 3 days, which function models this situation?

Accepted Answer

$$y = 2^{x/3}$$

Answer

$$y = 2x$$

Answer

$$y = x^2$$

Answer

$$y = (1/2)^x$$

Question 10

Suppose the function $$y=67,000(1.09)^x$$ models the annual profit for a small business x years after 2000. Find the profit at the end of 2020.(round to the nearest dollar)

Accepted Answer

about $375496

Answer

about $245000

Answer

about $333000

Answer

about $5

Question 11

A population of bacteria grows exponentially, and its population can be modeled by the function $$P(t) = P_0 \cdot 2^t$$ , where $$P_0$$ is the initial population and $$t$$ is time in hours. If the initial population is 100, what is the population after 3 hours?

Accepted Answer

800

Answer

200

Answer

400

Answer

600

Question 12

A car worth $$25,000$$ depreciates at a rate of 20% per year. What is the initial value of the car in the exponential decay function modeling this situation?

Accepted Answer

$$25,000$$

Answer

$$20,000$$

Answer

$$5,000$$

Answer

$$20\%$$

Question 13

The population of Boomtown is 10647 and is increasing at a rate of 3% each year. The exponential equation that represents the population of Boomtown after x years is $$p\left(x\right)=10647\left(1.03\right)^x$$ . When will the population exceed 30000 thousand people (to the nearest year)?

Accepted Answer

36

Answer

14

Answer

34

Answer

13

Question 14

Cassandra bought a car for $45,000. If the value of her car decreases 4% annually. The exponential function that best represents the value of the car after x years is $$g\left(x\right)=45000\left(0.96\right)^x$$ what will be the value of Cassandra's car at the end of 3 years to the nearest dollar?

Accepted Answer

$39813

Answer

$39814

Answer

$9700

Answer

$9720

Question 15

Ms. Peralta bought a new car, which cost her $27,000. Which equation represents the value of the car after 5 years, if the car depreciates at a rate of 20% per year?

Accepted Answer

$$A\left(5\right)=27000\left(1-0.20\right)^5$$

Answer

$$A\left(5\right)=27000\left(1+0.20\right)^5$$

Answer

$$A\left(5\right)=27000\left(1-5\right)^{0.20}$$

Answer

$$A\left(5\right)=27000\left(1-0.80\right)^5$$

Real World Exponential Equations

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