Question

A​ country's travel exports​ (good and services that international travelers buy while visiting the​ country) are increasing exponentially. The value of such​ exports, t years after​ 2011, can be approximated by ​V(t)equals111.83 e Superscript 0.088 t​, where V is in billions of dollars. ​a) Estimate the value of the​ country's travel exports in 2018 and 2020. ​b) Estimate the growth rate of the​ country's travel exports in 2018 and 2020.

Answer 1

(a)In 2018, V(t)=$207.05 billion

In 2020, V(t)=$246.90 billion

(b)The export growth rate in 2018 is $18.22 billion per year

The export growth rate in 2020is $21.73 billion per year

Step-by-step explanation:

The value of exports, t years after 2011 can be approximated by:

`V(t)=111.83 e^(0.088 t)`

(a)We want to estimate the value of the country's travel exports in 2018 and 2020.

Now, 2018-2011=7 years

Therefore, in 2018

`V(7)=111.83 e^(0.088 *7)\\=\$207.05$ billion`

Now, 2020-2011=9 years

Similarly, in 2020

`V(9)=111.83 e^(0.088 *9)\\=\$246.90$ billion`

(b)Growth rate

If
`V(t)=111.83 e^(0.088 t)`, then:

`V'(t)=111.83(0.088) e^(0.088 t)\\V'(t)=9.84104 e^(0.088 t)`

Growth rate in 2018 (at t=7)

`V'(7)=9.84104 e^(0.088*7)\\=\$18.22$ billion per year`

Growth rate in 2020 (at t=9)

`V'(9)=9.84104 e^(0.088*9)\\=\$21.73$ billion per year`