Respuesta :
Given:
The function is:
[tex]f(x)=2.9646(1.0170)^x[/tex]
To find:
Rewrite the exponential equation given above using base e.
Solution:
The exponential models is:
[tex]f(x)=P(1+r)^x[/tex] ...(i)
Where P is initial values, r is the rate of interest and x is the time period.
The exponential models using base e is:
[tex]f(t)=Pe^{rt}[/tex] ...(ii)
Where, P is initial values, r is the rate of interest and t is the time period.
The given function is:
[tex]f(x)=2.9646(1.0170)^x[/tex]
It can be written as:
[tex]f(x)=2.9646(1+0.0170)^x[/tex] ...(iii)
On comparing (i) and (iii), we get
[tex]P=2.9646[/tex]
[tex]r=0.0170[/tex]
Putting [tex]P=2.9646[/tex] and [tex]r=0.0170[/tex] in (ii), we get
[tex]f(t)=2.9646e^{0.0170t}[/tex]
Therefore, the correct option is D.
