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A function f(x) increases by a factor of 1.9 over every unit interval in x and f(0)=2.Which could be a function rule for f(x)?

Question

A function f(x) increases by a factor of 1.9 over every unit interval in x and f(0)=2. Which could be a function rule for f(x)?

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Solution

The function described is an exponential function. The general form of an exponential function is f(x) = ab^x, where a is the initial value and b is the growth factor.

Given that f(0) = 2, we know that a = 2 because any number raised to the power of 0 is 1, so f(0) = a * b^0 = a.

Also, we know that the function increases by a factor of 1.9 over every unit interval in x, which means b = 1.9.

So, a possible function rule for f(x) could be f(x) = 2 * 1.9^x.

This problem has been solved

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