Question

If f(x) is an exponential function where f(2)=23 and f(3)=58, then find the value of f(6), to the nearest hundredth.

Answer 1

The exponential function is given as 3.68 × (2.52)ˣ. Then the value of function at x = 6 will be 942.43.

What is an exponent?

The exponent denotes that the base will rise to a specific level of strength. The base is X, and the power is n.

If f(x) is an exponential function where f(2) = 23 and f(3) = 58.

Then the exponential function will be

f(x) = abˣ

If f(2) = 23, then we have

23 = ab² ...1

If f(3) = 58, then we have

58 = ab³ ...2

Then from equations 1 and 2, we have

a = 3.62 and b = 2.52

Then the function will be

f(x) = 3.68 × (2.52)ˣ

Then the value of f(6) will be

f(6) = 3.68 × (2.52)⁶

f(6) = 3.68 × 256.1

f(6) = 942.43

More about the exponent link is given below.

brainly.com/question/5497425

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