Quiz about Real World Exponential Problems

Question 1

You deposit $12,000 into a bank account that pays 0.75% annual interest, compounded monthly. How much money will you have after ten years?

Accepted Answer

$12,934.31

Answer

$13,456.01

Answer

$14,951.17

Answer

$12,521.84

Question 2

Jaime owns a side business detailing cars. His first year he made $10,500 dollars and each of the following years his profit increased by 9% . How much profit (money) will Jaime make after 12 years?

Accepted Answer

Initial value is $10500

Accepted Answer

Growth factor (base b) is 1.09

Accepted Answer

x represents time therefore x=12.

Answer

Growth factor (base b) is 1.90

Answer

The exponential equation is

$$f\left(x\right)=10500\left(9\right)^x$$

Question 3

Suppose you deposit $1000 in a college fund that pays 7.2% interest every year. The exponential function that best models the account balance after x number of years is $$f\left(x\right)=1000\left(1.072\right)^x$$ . Find the account balance after 5 years.

Accepted Answer

$1415.71

Answer

$15053.7

Answer

$1320.62

Answer

875.40

Question 4

A town with a population of 5,000 grows 3% per year. Find the population at the end of 10 years.

Hint: x represents time (years, months, days, hours).

Accepted Answer

6719.58

Answer

6149.37

Answer

68929.2

Answer

53022.5

Question 5

Your new computer cost $1500 but it depreciates (decrease) in value by about 18% each year.

How much will you computer be worth after 5 years?

Accepted Answer

$556.11

Answer

$827.052

Answer

$0.283435

Answer

$290.238

Question 6

The height of a tree h is increasing at a rate of 15% each year . If the original height of the tree was 40 feet, what would be the height of the tree after 3 years?

Accepted Answer

60.84 feet

Answer

52.9 feet

Answer

24.565 feet

Answer

13500 feet

Question 7

Grossi makes an initial investment of $5000. The investment loses 13% each year. Find the amount Grossi has at the end of 8 years. Hint: x represents time (years, months, days, hours).

Accepted Answer

1641.06

Answer

1641.87

Answer

13292.2

Answer

617.868

Question 8

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

Accepted Answer

$$y\ =\ 5000\left(1-\frac{30}{100}\right)^t$$

Answer

$$y\ =\ 5000\left(1+\frac{30}{100}\right)^t$$

Answer

$$y\ =\ 30\left(1-\frac{5000}{100}\right)^t$$

Answer

$$y\ =\ 30\left(1+\frac{5000}{100}\right)^t$$

Question 9

You invested $400 into an account with 7.5% interest rate compounded monthly. Which equation can be used to calculate how much you will have in 7 years?

Accepted Answer

$$f\left(x\right)\ =\ 400\left(1+\frac{7.5}{100}\right)^7$$

Answer

$$f\left(x\right)\ =\ 7.5\left(1+\frac{400}{100}\right)^7$$

Answer

$$f\left(x\right)\ =\ 400\left(1+\frac{7}{100}\right)^{7.5}$$

Answer

$$f\left(x\right)\ =\ 7\left(1+\frac{7.5}{100}\right)^{400}$$

Question 10

You have inherited land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. Write an equation to represent the situation:

Accepted Answer

$$f\left(x\right)\ =\ 30,000\left(1\ +\ 0.05\right)^t$$

Answer

$$f\left(x\right)\ =\ 30,000\left(1\ -\ 0.05\right)^t$$

Question 11

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

Accepted Answer

y=5000(0.7)^x

Answer

y=30(5000)^x

Answer

y=5000(1.3)^x

Answer

y=5000xx

Real World Exponential Problems

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