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Answer :
Final answer:
By using the recursive function f(n) = 4f(n-1) and beginning with given f(1) = 5, we can calculate the subsequent values until we arrive at f(6). Upon computation, the value of f(6) = 5120, which doesn't match any of the given choices.
Explanation:
The initial foundation for solving this problem is understanding the recursive function provided: f(n) = 4f(n-1). You are given that f(1) = 5. Meaning that when n = 1, the value of the function is 5. Now, as per the equation, every subsequent value of the function is 4 times the previous value. So, to find the value of f(6), you repeatedly apply the function on the given value f(1) = 5.
- f(2) = 4 * f(1) = 4*5 = 20
- f(3) = 4 * f(2) = 4 * 20 = 80
- f(4) = 4 * f(3) = 4 * 80 = 320
- f(5) = 4 * f(4) = 4 * 320 = 1280
- f(6) = 4*f(5) = 4 * 1280 = 5120
So, none of the given options a) 320 b) 160 c) 640 d) 80 are correct.
Learn more about Recursive Functions here:
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