Exponential Compounding Word Problems

Write an equation that models the following situation: Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week. (HINT: Write out the equation on a separate piece of paper and then simplify inside the parenthesis)

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

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

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:

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?

• $8,881.47

• $7,432.93

• $8,400

• $6,500

Does the following equation show growth or decay?
y=10,000*(1+.05)^x

• Growth 

• Decay

Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour, how many bacteria will we have after half of a day?

• 1024

• 2048

• 8192

• 4096

The population of Hickory NC, can be modeled by P=6191(1.04)t where t is the number of years since 1995. What was the population in 1995?

• 6191

• 1

• 1995

• 1.04

You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine?

• 16

• 17

• 18

• 19