Quiz about Real World Exponential Problems

Question 1

Is the table linear or exponential?

Accepted Answer

Exponential Table

Answer

Linear Table

Question 2

Is the table linear or exponential?

Accepted Answer

Exponential Table

Answer

Linear Table

Question 3

Is the table linear or exponential?

Accepted Answer

Exponential Table

Answer

Linear Table

Question 4

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

Accepted Answer

$12,749.30

Answer

$12712.31

Answer

$12,657.59

Answer

$12550.84

Question 5

Using logarithms to solve real-world problems: The value of a car depreciates by 10% each year. If the initial value of the car is $20,000, what will be its value after 5 years?

Accepted Answer

The value of the car after 5 years will be $12,861.30.

Answer

The value of the car after 5 years will be $25,000.

Answer

The value of the car after 5 years will be $18,000.

Answer

The value of the car after 5 years will be $22,000.

Question 6

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

Accepted Answer

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

Answer

Answer

$$y = x^2$$

Answer

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

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 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 9

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 10

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 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

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 13

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 14

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 15

Principal: $10,000

Interest Rate: 6.5%

Time: 10 years

Compounded Quarterly

State the future account balance.

Accepted Answer

$19,055.59

Answer

$10,749.30

Answer

$15,657.59

Answer

$17,550.87

Question 16

You deposit $2000 into a bank account that pays 2.25% annual interest, compounded semi-annually. How much money will you have after six years?

Accepted Answer

$2,287.35

Answer

$2,582.45

Answer

$2,312.34

Answer

$3, 679.92

Real World Exponential Problems

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