The explicit equation of the function is t(n) = 5 * 8^(n-1)
How to determine the explicit equation?
The function definition is given as:
t(1)=5
t(n+1)=8t(n)
Let n = 1
So, we have:
t(2) = 8t(1)
Divide through by t(1)
t(2)/t(1) = 8
The common ratio of the function is:
r = t(2)/t(1) = 8
The explicit rule is then calculated as:
t(n) = t(1) * r^(n-1)
So, we have:
t(n) = 5 * 8^(n-1)
Hence, the explicit equation of the function is t(n) = 5 * 8^(n-1)
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