# Applications of Exponential Functions (1 transform, positive base)

## 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.

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

Maria purchased an artwork for $£2000$£2000 as an investment. At the end of each year its value is $1.07$1.07 times its value at the beginning of the year. Its value $t$t years after purchase is given by $V=A\times1.07^t$V=A×1.07t.

The growth of a population of mice modelled by $P=20\left(3^x\right)$P=20(3x), where $P$P is the population after $x$x weeks.

After how many weeks, $x$x, will the population of mice have grown to $4860$4860?

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 penny.