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Grade 11

Contextual problems with exponentials III

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
2min

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.

Easy
1min

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?

Easy
1min

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.

Easy
2min
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Outcomes

11U.B.2.5

Represent an exponential function with an equation, given its graph or its properties

11U.B.3.2

Identify exponential functions, including those that arise from real-world applications involving growth and decay, given various representations

11U.B.3.3

Solve problems using given graphs or equations of exponential functions arising from a variety of real-world applications by interpreting the graphs or by substituting values for the exponent into the equations

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