Advanced MathHardWhere consecutive outputs of an exponential function differ by a given amount
Advanced Math practice question
The function f is defined by f(x) = 2^x. For what value of x is f(x + 1) − f(x) = 64?
Answer: 6
f(x + 1) − f(x) = 2^(x+1) − 2^x = 2^x(2 − 1) = 2^x. So 2^x = 64 = 2⁶ and x = 6.
Common wrong answers
- If you answered 5
- 5 comes from 2^x = 32, halving 64 unnecessarily.
- If you answered 7
- 7 is x + 1.
- If you answered 64
- 64 is the value of 2^x, not x.
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