Question

The mass of a particular substance is known to grow exponentially at a rate of 1.5% per day. Its initial mass was 230 grams and, after t days, it weighed 325 grams.

The equation modelling this growth is

230×1.015 t  =  325.

Use the method of taking logs to solve this equation for t, giving your answer correct to the nearest day.

Answer 1

23 days

Explanation:

Given that the mass of a particular substance is known to grow exponentially at a rate of 1.5% per day

Initial mass =
`230 gm`

After t days, mass =
`325 gm`

The equation is

`P(t) = 325 = 230 (1+(1.5)/(100) )^t\\(325)/(230) =1.015^t\\log 1.413 = t log 1.015\\t = (log 1.413)/(log 1.015) =(0.1502)/(0.0065) \\=23.229`

Approximately after 23 days the mass will become 325 gms.