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)?
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.
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