Final answer:
To find the value of a in the equation f(x) = ab^x, substitute the given values into the equation and solve for a.
Step-by-step explanation:
Exponential growth occurs when the rate of growth, as a percentage or fraction, is constant. In this case, the rate of growth is 10%. To find the value of a in the equation f(x) = ab^x, we can use the given information. Since the function grows exponentially at a rate of 10%, we can set b = 1 + 10/100 = 1.1. Now, we can substitute the value of x = 3 and f(x) = 665.5 into the equation to solve for a.
f(x) = ab^x
665.5 = a(1.1)^3
665.5 = 1.331a
a = 665.5/1.331
a ≈ 499.62
Therefore, the value of a in the equation f(x) = ab^x is approximately 499.62.