Question

The mass of a particular substance is known to grow exponentially at a rate of 17% per week. Its initial mass was 12 grams and, after t weeks, it weighed 56 grams. The equation modelling this growth is 12x1.17 56. Use the method of taking logs to solve this equation for t, giving your answer correct to the nearest week. (Your answer should be a number, without units) Answer:

Answer 1

`t = 9.05` weeks

Explanation:

The mass of this particular substance can be modeled by the following exponential function:

`m(t) = m(0)*e^(rt)`

In which
`m(t)` is the mass in function of time,
`m(0)` is the initial mass and r, in decimal, is the growth rate of the mass.

The problem states that:

The mass of a particular substance is known to grow exponentially at a rate of 17% per week. Its initial mass was 12 grams and, after t weeks, it weighed 56 grams. So:

`r = 17% = 0.17`

`m(0) = 12`

`m(t) = 56`

We have to solve this equation for t. So:

`m(t) = m(0)*e^(rt)`

`56 = 12*e^(0.17t)`

`e^(0.17t) = (56)/(12)`

`e^(0.17t) = 4.67`

To solve for
`t`, we put ln in both sides

`ln e^(0.17t) = ln 4.67`

`0.17t = 1.54`

`t = (1.54)/(0.17)`

`t = 9.05` weeks