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.