Download WWSQ: EXPONENTIAL GROWTH AND DECAY APPLICATION

WWSQ:
EXPONENTIAL GROWTH AND DECAY APPLICATION PROBLEMS
Watch the video (On HAIKU!) setting up the following problems.
nt
r

HalfLifeDe cayFormula
A  P1   A  final amount, P  amount deposited ,
t
 n
 1h
r  rate(asdecimal ), n  number of times compounded in 1 year A(t )  Ao   A  final amount, Ao  originalam ount ,
2
t  time, h  halflife
1. The mice population is 25,000 and is decreasing by 20% each year.
a. Write an equation to model the population P after t years.
b. What will the population be after 3 years?
2. The number of mosquitoes at the beach has tripled every year since 1999. In 1999, there were 2,500
mosquitoes.
a. Write an equation to model the number of mosquitoes M, t years after 1999.
b. How many mosquitoes will there be in 2005?
3. If I have $500 in my account after 4 years of investment at 2.5% compounded annually,
a. Write an equation to model the amount A after t years.
b. How much money did I start with?
4. You deposit $1500 in an account that pays 5% interest compounded yearly.
a. Write an equation to model the amount A after t years.
b. How much money did I start with?
5.
The number of bacteria in a culture is modeled by the function n(t )  500(2.718) 0.45t where t is
measured in hours. (FYI a base of 2.718 is also known as “e”…more to follow)
a.
What is the initial number of bacteria?
b. What is the relative rate of growth of this bacterium population? Express your answer as a
percentage.
c. How many bacteria are present in the culture after 3 hours?
d. After how many hours will the number of bacteria reach 10,000?
6. 3 Polonium-210 has a half-life of 140 days. Suppose a sample of this substance has a mass of 300 mg.
a. Find a function that models the amount of the sample remaining at time t days.
b. Find the mass remaining after 1 year.
c. How long will it take for the sample to decay to a mass of 200 mg?
7.
The deer population at the local reserve grows exponentially. The current population is 125 deer and
the relative growth rate is 16% a year.
a. Write an equation to model the population P, after t years.
b. Find the number of years required for the deer population to be 400.
WWSQ:
EXPONENTIAL GROWTH AND DECAY APPLICATION PROBLEMS
Watch the video (On HAIKU!) setting up the following problems
nt
r

A  P1   A  final amount, P  amount deposited ,
 n
r  rate(asdecimal ), n  number of times compounded in 1 year
HalfLifeDe cayFormula
t
 1h
A(t )  Ao   A  final amount, Ao  originalam ount ,
2
t  time, h  halflife
1. The mice population is 25,000 and is decreasing by 20% each year.
a. Write an equation to model the population P after t years.
b. What will the population be after 3 years?
2. The number of mosquitoes at the beach has tripled every year since 1999. In 1999, there were
2,500 mosquitoes.
a. Write an equation to model the number of mosquitoes M, t years after 1999.
b. How many mosquitoes will there be in 2005?
3. If I have $500 in my account after 4 years of investment at 2.5% compounded annually,
a. Write an equation to model the amount A after t years.
b. How much money did I start with?
4. You deposit $1500 in an account that pays 5% interest compounded yearly.
a. Write an equation to model the amount A after t years.
b. How much money did I start with?
5.
The number of bacteria in a culture is modeled by the function n(t )  500(2.718) 0.45t where t is
measured in hours. (FYI a base of 2.718 is also known as “e”…more to follow)
a. What is the initial number of bacteria?
b. What is the relative rate of growth of this bacterium population? Express your answer as a
percentage.
c. How many bacteria are present in the culture after 3 hours?
d. After how many hours will the number of bacteria reach 10,000?
6. 3 Polonium-210 has a half-life of 140 days. Suppose a sample of this substance has a mass of 300
mg.
a. Find a function that models the amount of the sample remaining at time t days.
b. Find the mass remaining after 1 year.
c. How long will it take for the sample to decay to a mass of 200 mg?
7.
The deer population at the local reserve grows exponentially. The current population is 125 deer
and the relative growth rate is 16% a year.
a. Write an equation to model the population P, after t years.
b. Find the number of years required for the deer population to be 400.