Question

Evaluating and solving functions

Use the function f(x)=240(0.7)^x to answer the following questions. Round your nearest answers to two decimal places.
Evaluate f(7) f(7)=
Determine x when f(×)=120

Answer 1

Evaluate f(7)

`f(7) = 240(0.7)^7 = 19.765`

Determine x when f(×)=120

`120 = 240 (0.7)^x`

We can derive both sides by 240 and we got:

`0.5 = 0.7^x`

Now we can apply natural log on both sides and we got:

`ln(0.5)= x ln(0.7)`

And if we solve for the value of x we got:

`x =(ln(0.5))/(ln(0.7))= 1.943`

And then the value of x = 1.943

Explanation:

We have the following function given:

`f(x) = 240(0.7)^x`

Evaluate f(7)

And we want to find
`f(7)` so we just need to replace x=7 and we got:

`f(7) = 240(0.7)^7 = 19.765`

Determine x when f(×)=120

And for the second part we want to find a value of x who satisfy that the function would be equal to 120 and we can set up this:

`120 = 240 (0.7)^x`

We can derive both sides by 240 and we got:

`0.5 = 0.7^x`

Now we can apply natural log on both sides and we got:

`ln(0.5)= x ln(0.7)`

And if we solve for the value of x we got:

`x =(ln(0.5))/(ln(0.7))= 1.943`

And then the value of x = 1.943