Respuesta :
Answer:
Therefore the initial amount will be doubled after 19.8 years.
Step-by-step explanation:
Given that,
The amount of money increases according to the following function
[tex]y=y_0e^{0.035t}[/tex]
where [tex]y_0[/tex] = the initial amount of the investment, and y = the amount present at time t (in years).
Let after t years the initial amount will be double.
[tex]\therefore y=2 y_0[/tex], t=t
[tex]y=y_0e^{0.035t}[/tex]
[tex]\Rightarrow 2y_0=y_0e^{0.035t}[/tex]
[tex]\Rightarrow 2=e^{0.035t}[/tex]
Taking ln both sides
[tex]\Rightarrow ln(2)=ln(e^{0.035t})[/tex]
[tex]\Rightarrow ln(2)={0.035t}[/tex] [ [tex]\because lne^a=a[/tex]]
[tex]\Rightarrow t=\frac{ln(2)}{0.035}[/tex]
[tex]\Rightarrow t=19.8[/tex] years
Therefore the initial amount will be doubled after 19.8 years.
The number of years it would take the initial investment to double is 19.8 years.
The formula used to calculate the value of an investment after a specified number of years with continuously compounded interest is:
FV = A x [tex]e^{r}[/tex] x N
- A= amount
- e = 2.7182818
- N = number of years
- r = interest rate
- FV = future value
y = [tex]y_{0}[/tex] x [tex]e^{0.035}[/tex]t
y / [tex]y_{0}[/tex] = 2
log(2) ÷ log(e) ÷ 0.035
= 19.8 years
A similar question was answered here: https://brainly.com/question/19198922
