Quiz about Algebra 1: Linear vs. Exponential Functions

Question 1

For the function $$c\left(t\right)=1000\left(0.75\right)^t$$ , determine if it represents exponential growth or decay AND determine the percent increase/decrease.

Accepted Answer

decay:

25% decrease

Answer

growth:

75% increase

Answer

growth:

25% increase

Answer

decay:

75% decrease

Question 2

A tennis tournament has 128 competitors. Half of the competitors are eliminated each round. Write an equation to represent the number of competitors left after x rounds.

Accepted Answer

$$y=128\left(\frac{1}{2}\right)^x$$

Answer

$$y=128-64x$$

Answer

$$y=128-\frac{1}{2}x$$

Question 3

Determine if the following is an example of a linear OR exponential situation:

Suzy adds $10 to her piggy bank each week.

Accepted Answer

Linear

Answer

Exponential

Answer

Neither

Question 4

A three-bedroom house in Burbville was purchased for $190,000. If housing prices are expected to increase by 2% annually in Burbville, write an equaion to represent the price of the house after x years.

Accepted Answer

$$y=190,000\left(1.02\right)^x$$

Answer

$$y=190,000\ +\ 2x$$

Answer

$$y=190,000\cdot2x$$

Answer

$$y=190,000\left(1.2\right)^x$$

Question 5

For the function $$p\left(n\right)=40\left(1.80\right)^n$$ , determine if it represents exponential growth or decay AND determine the percent increase/decrease.

Accepted Answer

growth:

80% increase

Answer

growth:

8% increase

Answer

decay:

80% decrease

Answer

decay:

20% decrease

Question 6

Jonathan makes a weekly allowance of $25. He also makes $9.50 per hour at his job. Write an equation to represent the amount of money earned in a week if he works for x hours in a week.

Accepted Answer

$$y=25+9.50x$$

Answer

$$y=9.50+\ 25x$$

Answer

$$y=25\left(9.50\right)^x$$

Question 7

Determine if the following is an example of a linear OR exponential situation:

A certificate of deposit earns 4% interest each year.

Accepted Answer

Exponential

Answer

Linear

Answer

Neither

Question 8

Kelli's mom takes a 400 mg dose of aspirin. Each hour, the amount of aspirin in a person's system decreases by about 29%. Write an equation to represent the amount of aspirin left in her system x hours after she took the aspirin.

Accepted Answer

$$y=400\left(0.71\right)^x$$

Answer

$$y=400\left(1.29\right)^x$$

Answer

$$y=400-29x$$

Answer

$$y=400\left(0.29\right)^x$$

Question 9

For the function $$t\left(x\right)=10,000\left(1.02\right)^x$$ , determine if it represents exponential growth or decay AND determine the percent increase/decrease.

Accepted Answer

growth:

2% increase

Answer

growth:

0.2% increase

Answer

decay:

98% decrease

Answer

decay:

2% decrease

Question 10

The value of an early American coin increases in value at a rate of 6.5% annually. If the purchase price of the coin this year is $1,950, write an equation to model the value in x years.

Accepted Answer

$$y=1950\left(1.065\right)^x$$

Answer

$$y=1950\left(0.935\right)^x$$

Answer

$$y=1950+6.5x$$

Answer

$$y=1950+1.65x$$

Question 11

Determine if the following is an example of a linear OR exponential situation:

$150 is deducted from your savings account each month.

Accepted Answer

Linear

Answer

Exponential

Answer

Neither

Question 12

Kate's grandparents got her a piggy bank when she was born with $100 inside. Each year Kate adds $60 to the piggy bank. Write an equation to represent amount of money in her account after x years.

Accepted Answer

$$y=100+60x$$

Answer

$$y=100\left(0.6\right)^x$$

Answer

$$y=60+100x$$

Question 13

For the function $$f\left(n\right)=50\left(0.1\right)^n$$ , determine if it represents exponential growth or decay AND determine the percent increase/decrease.

Accepted Answer

decay:

90% decrease

Answer

growth:

10% increase

Answer

growth:

90% increase

Answer

decay:

10% decrease

Question 14

You need $200 to start a snow cone stand for the summer. You borrow the money from a bank that charges 4% interest compounded monthly. Choose the expression that represents the amount owed after 3 years.

Accepted Answer

$$200\left(\left(1+\frac{0.04}{12}\right)^{12}\right)^3$$

Answer

$$200\left(\left(1.04\right)^{12}\right)^3$$

Answer

$$200\left(\left(1+\frac{0.04}{3}\right)^3\right)^{12}$$

Question 15

Determine if the following is an example of a linear OR exponential situation:

The value of a house increases in value by 1.5% each year.

Accepted Answer

Exponential

Answer

Linear

Answer

Neither

Question 16

Kyra has been babysitting since 6th grade. She has saved $1000 and wants to open an account at the bank where she earns 10% interest, compouded quarterly. Choose the expression that represents the amount of money Kyra will have after 2 years.

Accepted Answer

$$1000\left(\left(1+\frac{0.10}{4}\right)^4\right)^2$$

Answer

$$1000\left(\left(1+\frac{0.10}{2}\right)^2\right)^4$$

Answer

$$1000\left(1.10\right)^8$$

Question 17

What type of function is shown in the graph?

Accepted Answer

Exponential Growth

Answer

Linear

Answer

Exponential Decay

Question 18

Malik bought a new car for $15,000. He was told that the car's value will decrease by 15% every year. Write an equation to represent the car's value after x years.

Accepted Answer

$$y=15,000\left(0.85\right)^x$$

Answer

$$y=15000-15x$$

Answer

$$y=15,000\left(0.15\right)^x$$

Answer

$$y=15,000-85x$$

Question 19

Determine if the following is an example of a linear OR exponential situation:

The amount of money in Jacyln's wallet increases and decreases by different amounts each week.

Accepted Answer

Neither

Answer

Linear

Answer

Exponential

Question 20

What type of function is shown in the graph?

Accepted Answer

Linear

Answer

Exponential Growth

Answer

Exponential Decay

Algebra 1: Linear vs. Exponential Functions

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