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New Zealand
Level 7 - NCEA Level 2

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
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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



Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs


Manipulate rational, exponential, and logarithmic algebraic expressions


Apply graphical methods in solving problems


Apply algebraic methods in solving problems

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