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Stage 4 - Stage 5

Applications of Exponential Functions

Interactive practice questions

The formula $A=1000\times2^t$A=1000×2t models the population, $A$A, of aphids in a field of potato plants after $t$t weeks. Use this formula to solve the following questions.


What is the present aphid population?


What will the aphid population be in $5$5 weeks?


What was the aphid population $2$2 weeks ago?

Approx 2 minutes

The population, $P$P, of a particular town after $n$n years is modelled by $P=P_0\left(1.6\right)^n$P=P0(1.6)n, where $P_0$P0 is the original population.

Find the population of the town after $3\frac{1}{2}$312 years if its original population was $30000$30000. Give your answer to the nearest whole number.

A fixed-rate investment generates a return of $6%$6% per annum, compounded annually. The value of the investment is modelled by $A=P\left(1.06\right)^t$A=P(1.06)t, where $P$P is the original investment.

Find the value of the investment after after $3\frac{1}{4}$314 years if the original investment was $\$200$$200. Give your answer to the nearest cent.

A car originally valued at $\$28000$$28000 is depreciated at the rate of $15%$15% per year. The salvage value $S$S of the car after $n$n years is given by $S=28000\left(1-\frac{15}{100}\right)^n$S=28000(115100)n

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