High School

If [tex]f(c)[/tex] is an exponential function where [tex]f(3) = 11[/tex] and [tex]f(5.5) = 57[/tex], then find the value of [tex]f(10.5)[/tex] to the nearest hundredth.

A. 374.94
B. 163.29
C. 164.84
D. 368.50

Answer :

Final answer:

To find the value of f(10.5) in an exponential function, calculate the growth factor and use it in the exponential formula with the given initial values. The correct result is 374.94 (option a).

Explanation:

The value of f(10.5) in relation to the given exponential function can be found by using the exponential growth formula:

  1. First, calculate the growth factor (k) using the initial and final values given: k = f(5.5)/f(3) = 57/11.
  2. Next, substitute the growth factor into the exponential function: f(c) = f(3) * (k)^(c-3).
  3. Finally, plug in c = 10.5 to find the value of f(10.5) to the nearest hundredth.

Therefore, the correct value of f(10.5) is approximately 374.94, which is option a).

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