Respuesta :
Using an exponential function, we have that:
a) In 10 years, the amount needed will be of $1,219 per week.
b) In 20 years, the amount needed will be of $1,486 per week.
c) In 30 years, the amount needed will be of $1,811 per week.
An increasing exponential function has the following format:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
- A(0) is the initial value.
- r is the rate of change, as a decimal.
In this problem:
- Currently requires $1000, thus [tex]A(0) = 1000[/tex].
- Inflation of 2% per year, thus [tex]r = 0.02[/tex]
Then, his weekly amount needed is going to be given by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 1000(1 + 0.02)^t[/tex]
[tex]A(t) = 1000(1.02)^t[/tex]
Item a:
In 10 years, we have that:
[tex]A(10) = 1000(1.02)^{10} = 1219[/tex]
In 10 years, the amount needed will be of $1,219 per week.
Item b:
In 20 years, we have that:
[tex]A(20) = 1000(1.02)^{20} = 1486[/tex]
In 20 years, the amount needed will be of $1,486 per week.
Item c:
In 30 years, we have that:
[tex]A(30) = 1000(1.02)^{30} = 1811[/tex]
In 30 years, the amount needed will be of $1,811 per week.
A similar problem is given at https://brainly.com/question/21942338
