Continuous Growth and Decay Word Problems

Miguel had 25 bacteria in his petri dish at 2 PM. There were 72 in the dish at 2:30 PM. Assuming exponential growth, at what rate are they increasing?

• 9.6% per minute

• 0.03526% per minute

• 35.26% per minute

• 3.526% per minutes

The population of Guyana was roughly 787,000 in 2020 and 747,000 in 2000. If the population is growing exponentially, what is the rate of growth?

• 0.002608

• 0.00113

• 0.0527

• .2608

If a population of 300 animals in a certain region is growing exponential at 2% per year, when will the population reach 400?

• 14.4 years

• 15 years

• 6.2 years

• 20 years

A new computer continuously loses about 45% of its value each year. If Monique spent $1600 on her computer, how much will it be worth in 5 years?

• $1420.00

• $146.31

• $65.61

• $168.64

Using the exponential function equation f(x)=ab^x, where a is the starting value and b is the growth or decay, and x is the time, find the value of a house after 15 years if it initially worth $250,000 and increases by 5% each year.

• $405,518.75

• $500,000

• $425,000

• $375,000

Using the exponential function equation f(x)=ab^x, where a is the starting value and b is the growth or decay, and x is the time, find the population of fish after 8 weeks if the population doubles every week and initially there are 1000 fish.

• 128000

• 512000

• 64000

• 256000

Using the exponential function equation f(x)=ab^x, where a is the starting value and b is the growth or decay, and x is the time, find the population of bacteria after 5 hours if it doubles every hour and initially has 100 bacteria.

• 500

• 3200

• 2000

• 1000

The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?

• 29 to 30 days

• 23 to 24 days

• 15 to 16 days

• 19 to 20 days

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What is the population of the town 21 years later?

• 6191

• 9912

• 72519

• 14108

You have inherited a house that was purchased for $100,000 in 2010. The value of the house increased by approximately 2% per year. What is the approximate value of the house 11 years later ?

• $124,337

• $80,073

• $743,008

• $138,423