Exponentials

Hong Kong

Stage 4 - Stage 5

The formula $A=1000\times2^t$`A`=1000×2`t` 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.

a

What is the present aphid population?

b

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

c

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

Easy

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`=`P`0(1.6)`n`, where $P_0$`P`0 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(1−15100)`n`

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