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.

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=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

### Outcomes

#### M7-2

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

#### M7-6

Manipulate rational, exponential, and logarithmic algebraic expressions

#### 91257

Apply graphical methods in solving problems

#### 91261

Apply algebraic methods in solving problems