Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 14: Practice 4

Radioactive substances decay over time and are often described by their half-life (the time taken for half of the substance to decay/disappear). The formula used to describe this decay is $A=A_0{\mathrm{e}}^{-0.0866t}$, where $A$ is the amount left after time $t,A_0$ is the original amount of the radioactive substance. It is a common substance used in diagnosing issues with the thyroid gland. Find how many grams of iodine-$131$  will be present after $28$ days if you start with $3$ grams. [Use $e^{-2.4248}=0.8849$]

A group of 20 rabbits is introduced to a rabbit farm. After t years the number of rabbits, N. is modelled by the exponential equation $N=20e^{0.6t}$. Predict the number of rabbits after 3 years.

A group of 20 rabbits is introduced to a rabbit farm. After t years the number of rabbits, N. is modelled by the exponential equation $N=20e^{0.6t}$. Determine how long it will take for the number of rabbits to reach 400. Give your answers to an appropriate degree of accuracy.

The model for the population, P. of wombats in a nature reserve is $P=50e^{0.8t}$, where is measured in years. Write down how many wombats were introduced to the reserve

The model for the population, P. of wombats in a nature reserve is $P=50e^{0.8t}$, where is measured in years.

Calculate how long it will take for the original population to quadruple.

The population of a small Dutch town was obtained for two consecutive years:

Assume that the population is modelled by the standard equation, and that

Calculate the rate of grow

The population of a small Dutch town was obtained for two consecutive years:

Assume that the population is modelled by the standard equation, and that

Calculate the predicted population in 2020

The population of a small Dutch town was obtained for two consecutive years:

Assume that the population is modelled by the standard equation, and that

Calculate the number of years until the population Founds 10000.