Question

Need help with exponential functions for a test!!!!!

The growth of a certain organism can be modeled by C(t)=10(1.029)^24t, where C(t) is the total number of cells after t hours. Which function is approximately equivalent to C(t)?

1. C(t) =240(0.083)^24t
2. C(t)=10(.083)^t
3. C(t)=10(1.986)^t
4. C(t)= 240(1.986)^t/24

Answer 1

c

Explanation:

Answer 2

Given:

The function is:

`C(t)=10(1.029)^(24t)`

Where, C(t) is the total number of cells after t hours.

To find:

The function that is approximately equivalent to C(t).

Solution:

We have,

`C(t)=10(1.029)^(24t)`

It can be rewritten as:

`C(t)=10(1.029^(24))^(t)`
`[\because (a^m)^n=a^(mn)]`

`C(t)\approx 10(1.986)^(t)`
`[\because 1.029^(24)\approx 1.986]`

The function
`C(t)=10(1.986)^(t)` is approximately equivalent to C(t).

Therefore, the correct option is 3.