Respuesta :
Answer:
(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 $21.73 billion per year
Explanation:
The value of exports, t years after 2011 can be approximated by:
[tex]V(t)=111.83 e^{0.088 t}[/tex]
(a)We want to estimate the value of the country's travel exports in 2018 and 2020.
Now, 2018-2011=7 years
Therefore, in 2018
[tex]V(7)=111.83 e^{0.088 *7}\\=\$207.05$ billion[/tex]
Now, 2020-2011=9 years
Similarly, in 2020
[tex]V(9)=111.83 e^{0.088 *9}\\=\$246.90$ billion[/tex]
(b)Growth rate
If [tex]V(t)=111.83 e^{0.088 t}[/tex], then:
[tex]V'(t)=111.83(0.088) e^{0.088 t}\\V'(t)=9.84104 e^{0.088 t}[/tex]
Growth rate in 2018 (at t=7)
[tex]V'(7)=9.84104 e^{0.088*7}\\=\$18.22$ billion per year[/tex]
Growth rate in 2020 (at t=9)
[tex]V'(9)=9.84104 e^{0.088*9}\\=\$21.73$ billion per year[/tex]
