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A function f(t) increases by a factor of 9 over every unit interval in t and f(0)=1.Which could be a function rule for f(t)?

Question

A function f(t) increases by a factor of 9 over every unit interval in t and f(0)=1.Which could be a function rule for f(t)?

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Solution

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

Given that f(0) = 1, we know that a = 1.

Also, we know that the function increases by a factor of 9 over every unit interval in t, which means b = 9.

So, a possible function rule for f(t) could be f(t) = 1*9^t or simply f(t) = 9^t.

This problem has been solved

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