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(2n−2)+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.
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.
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)n−49.
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.