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Answer :
Final answer:
Using the given points f(0) = 100 and f(1) = 170, we determined that a = 100 and k ≈ 0.53 by solving exponential equations. The closest matching option for the function is f(x) = 100e^(0.7x).
Explanation:
To find the function f such that f(x) = aekx given that f(0) = 100 and f(1) = 170, we will use the given points to determine the values of a and k.
First, using f(0) = 100, we have:
f(0) = aek*0 = a*1 = a, thus a = 100.
Next, using f(1) = 170, we have:
f(1) = 100ek*1 = 100ek = 170, which implies ek = 170/100 = 1.7.
Taking the natural logarithm of both sides gives us k ≈ 0.53.
Therefore, the function that fits the given conditions is f(x) = 100e0.53x.
However, since this value 0.53 is not exactly represented in the options provided, we need to pick the closest option, which is: f(x) = 100e0.7x (Option d)
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