Answer :

Final answer:

To find the value of 'b' in the exponential function, we incorporate the given values into the function which results in two equations. After dividing these equations and solving, we find the value of 'b' to be approximately 2.23.

Explanation:

The problem belongs to the category of exponential equations.

Step 1: Start by inserting the given values into the equation f(x) = a(b)^x, which gives us[tex]15 = a(b)^5\ and \ 170 = a(b)^8.[/tex]

Step 2: Divide the two equations we got in step 1. Thus, we get [tex]170/15 = b^3,[/tex] which equates to [tex]11.33 \approx b^3[/tex]

Step 3: Take the cube root of both sides of the equation, which will give us the value of b as approximately 2.23.

Therefore, by solving the exponential equations, it can be concluded that the value of b is approximately 2.23 when f(5)=15 and f(8)=170.

Learn more about Exponential Equations here:

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Rewritten by : Barada

If f(x)=a(b)^x where f(5)=15 and f(8)=170

f(5) = 15 = a 5^x

f(8) = 170 = a8^x

divide

170 = a8^x

----------------

15 = a 5^x



34/3 = (8/5)^x

b = (8/5)