Question

The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. A sample increases

continuously at a relative rate of 11% per day. Find the mass of the sample after six days if there were 165 grams of the
substance present at the beginning of the study.

Answer 1

The mass of the sample after six days will be of 319.24 grams.

Explanation:

The exponential growth model for the mass of a substance after t days is:

`M(t) = M(0)e^(rt)`

In which M(0) is the initial mass and r is the increase rate, as a decimal.

A sample increases continuously at a relative rate of 11% per day.

This means that
`r = 0.11`

Find the mass of the sample after six days if there were 165 grams of the substance present at the beginning of the study.

This is M(6) when M(0) = 165.

`M(t) = M(0)e^(rt)`

`M(6) = 165e^(0.11*6)`

`M(6) = 319.24`

The mass of the sample after six days will be of 319.24 grams.