Question

Modeling Exponential Growth and Decay In Exercises 119 and 120, Find the exponential function

y = Cekt
that passes through the two given points.
(1, 1) (5, 5)

Answer 1

There is no exponential function passing through (1,1) and (5,5).

Explanation:

We have the following exponential function

`y = Ce^(kt)`

The function passes through these two points:

(1,1): This means that when t = 1, y = 1

(5,5): This means that when t = 5, y = 5.

So

(1,1)

`y = Ce^(kt)`

`Ce^(k) = 1`

`e^(k) = (1)/(C)`

(5,5)

`y = Ce^(kt)`

`5Ce^(k) = 1`

`Ce^(k) = (1)/(5)`

From above, we have that:

`e^(k) = (1)/(C)`

`C(1)/(C) = (1)/(5)`

`1 = (1)/(5)`

1 cannot be equal to 1/5, so this is wrong.

This means that there is no exponential function passing through (1,1) and (5,5).