Question

A certain country's consumer price index is approximated by a(t) = 100e0.024t, where t represents the number of years. use the function to determine the year in which costs will be 50% higher than in year 0.

Answer 1

`\boxed{\text{Year 17}}`

Explanation:

`a(t) = 100e^(0.024t)`

Data:

a(t) = 150

a(0) = 100

Calculations :

`\begin{array}{rcll}150 & = & 100e^(0.024t) & \\\\1.50 & = & e^(0.024t) & \text{Divided each side by 100}\\0.4055 & = & 0.024t & \text{Took the ln of each side}\\t & \approx & \mathbf{17} & \text{Divided each side by 0.024}\\\end{array}`

`\text{The consumer price index will be 50 \% higher in } \boxed{\textbf{year 17}}`