growth and decay functions exponential functions

Growth and decay functions

Exponential functions


1. A building society calculates the amount ‘A’ of money in Mr. Smith’s account by using the formula A(n) = 800 1.02n,

where n is the number of years the money has been in the account.

a) How much did Mr. Smith deposit initially?

b) What rate of interest were they paying?

c) How much will he have in his account after (i) 6 years (ii) 10 years.


2. A rabbit population on an island was studied over a period of time. The initial population was estimated

at 5600 and this was thought to be rising by 4% each year.

a) Construct a growth function for the number of rabbits.

b) Use this function to estimate the number of rabbits after (i) 5 years (ii) 10 years.

c) How long will it take for the rabbit population to double?


3. A fish colony consists of 8000 young fish. Each day the fish population decreases by 6% due to disease, predators etc.

a) Construct a decay function to estimate the population after n days.

b) Use this function to estimate the number of fish surviving after (i) 4 days (ii) 7 days.

c) After how many days does the fish population fall below 4000?


4. An outbreak of an infection carrying fly is reported in Peru. The initial estimate of people infected by the fly

is put at 400 with expected increase in numbers of 8% per day. Construct a growth function to estimate the number of expected

cases of infection. Use it to determine

a) Number of cases after (i) 3 days (ii) 7 days.b) If within two weeks the number of cases reported has tripled then an ‘epidemic’ is declared. Is there a need to declare an

epidemic for this outbreak?

5. On an island 2400 frogs are released into the wild. Each month 9% of the frogs perish through natural causes

such as predators. Determine a decay function which will describe ,in the short term,

the population of frogs on the island. a) What is the population after (i) 2 months (ii) 5 months?

b) How long will it take for the population to fall below1000 frogs?


6. An antique is valued at ₤48000. Each year it is expected to increase in value by

4% of its value at the start of that year. Set up a growth function to determinethe value of the antique after n years.

Use this function to determine the value after (i) 4 years (ii) 7 years.


7. A bottle contains 200ml of a very expensive perfume. By mistake the top is left off the bottle.

The perfume evaporates at the rate of 1% per hour.

Set up a decay function for the quantity of perfume remaining in the bottle and use it to determine the

volume of perfume remaining after (i) 6 hours (ii) 12 hours.


8. The seal population on a small island off the North coast of Scotland is estimated at 18500.

The numbers of seals inhabiting the island is being affected by oil pollution and a decrease in numbers each month of 5% per month for the foreseeable future is expected. Set up a decay function to monitor the seal population

and use it to estimate the number of seals each month for the next 8 months.


9. There are 80 grams of a radioactive material. Each year an amount of 6% is lost as the

material emits radioactive particles.

Set up a decay function to determine the amount of material left after n years.

Use this function to determine the amount of material left after (i) 4 years (ii) 10 years.


growth and decay functions exponential functions

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