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1.03 Applications of exponential functions

Interactive practice questions

The astronomical unit (AU) is often used to measure distances within the solar system. One AU is equal to the average distance between Earth and the Sun, or $92955630$92955630 miles. The distance, $d$d, of the $n$nth planet from the Sun can be modeled by the formula

$d=\frac{3\left(2^{n-2}\right)+4}{10}$d=3(2n2)+410

where $d$d is measured in astronomical units.

By substituting $2$2 for $n$n, find the distance between Venus and the Sun. Express your answer as a decimal, correct to two decimal places.

Easy
1min

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.

Easy
2min

The frequency $f$f (Hz) of the $n$nth key of an $88$88-key piano is given by $f\left(n\right)=440\left(2^{\frac{1}{12}}\right)^{n-49}$f(n)=440(2112)n49.

Medium
5min

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.

Easy
1min
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Outcomes

3.2.1.2

recognise that 𝑒 is the unique number 𝑎 for which the limit (in 3.2.1.1) is 1

3.2.1.5

identify contexts suitable for mathematical modelling by exponential functions and their derivatives and use the model to solve practical problems; verify and evaluate the usefulness of the model using qualitative statements and quantitative analysis

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