Question

Suppose the function:

f(x) = 2.9646 (1.0170)x

models the world population x years after 1948.

Rewrite the exponential equation given above using base e.

f(t) = 2.9646 e ^(0.0169) t


B.
f(t) = 2.9646 (1.0170) e^t


C.
f(t) = 2.9646 + 1.0170e^t


D.
f(t) = 2.9646 e^(1.0170t)


E.
f(t) = 2.9646 e^ln (1.0170t)

Answer 1

Given:

The function is:

`f(x)=2.9646(1.0170)^x`

To find:

Rewrite the exponential equation given above using base e.

Solution:

The exponential models is:

`f(x)=P(1+r)^x` ...(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:

`f(t)=Pe^(rt)` ...(ii)

Where, P is initial values, r is the rate of interest and t is the time period.

The given function is:

`f(x)=2.9646(1.0170)^x`

It can be written as:

`f(x)=2.9646(1+0.0170)^x` ...(iii)

On comparing (i) and (iii), we get

`P=2.9646`

`r=0.0170`

Putting
`P=2.9646` and
`r=0.0170` in (ii), we get

`f(t)=2.9646e^(0.0170t)`

Therefore, the correct option is D.