New Zealand
Level 7 - NCEA Level 2

# 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$$2000 as an investment. At the end of each year its value is 1.071.07 times its value at the beginning of the year. Its value tt years after purchase is given by V=A\times1.07^tV=A×1.07t. The growth of a population of mice modelled by P=20\left(3^x\right)P=20(3x), where PP is the population after xx weeks. After how many weeks, xx, will the population of mice have grown to 48604860? A fixed-rate investment generates a return of 6%6% per annum, compounded annually. The value of the investment is modelled by A=P\left(1.06\right)^tA=P(1.06)t, where PP is the original investment. Find the value of the investment after after 3\frac{1}{4}314 years if the original investment was \200$$200. Give your answer to the nearest cent.

### 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