Exponential Growth and Decay Formula

Which formula would you use for the following problem? Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

Which formula would you use for the following problem? Cora invested $400 at a rate of 35% for 8 months, compounded continuously. How much is her investment worth after 8 months?

Which formula would you use for the following problem? If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

Emily is culturing bacteria that have a growth rate of 5% per hour. If the current population is 36,000 bacteria, how many bacteria will there be in 12 hours? If necessary, round your answer to the nearest whole number.

• 8,789,062 bacteria.

• 19,452 bacteria.

• 61,572 bacteria.

• 64,651 bacteria.

The number of research papers in Professor Sycamore area of expertise has been increasing by 5% every year. Given that 30,010 research papers were published this year. Assuming the trend continues, which equation projects the amount of research papers published in x years?

• y = 30,010 (.05)^x

• y = 30,010 (1.05)^x

• y = 30,010 (.95)^x

• y = 30,010 (5)^x

• A

• B

• C

• D

This is an example of.....

• exponential decay

• exponential growth

• constant change

• a linear function

What is the growth factor of the situation represented by f(x)=10(0.3)^x?

• 10

• 0.3

• 1

• 3

Match each formula on the right

to the situation in which you would use it.

a

b

c

d

Compound Interest Formula

Continuously Compounding Interest

Basic Exp Growth Equation

Basic Exp Decay Equation

A population of fish starts at 8,000 and decreases by 6% per year. Write the exponential function that models this situation.

y = ​ (a)   (​ (b)   )^x

• 0.06

• 6

• 1.06

• 8000

• 0.94

• 480