Problem 1 · Use equal spacing to recover exponential growth · 3 points
Made by AI and not reviewed by a real person.
An increasing exponential function f has f(0) + f(2) = 25 and f(1) = 10. What is f(3)?
- 30
- 5/2
- 35
- 20
- 40
Show a hint
- Look at the three equally spaced inputs 0, 1, and 2. How does the middle value relate to the two outer values?
- For an exponential function, f(1)² = f(0)f(2). Use that with the given sum, then decide which outer value is larger.
Show the answer and solution
Answer: E — 40
The outer values have sum 25 and product f(1)² = 100, so they are 5 and 20. Since f is increasing, f(0) = 5 and f(2) = 20. Each step therefore doubles the value, giving f(3) = 40. The tempting 5/2 comes from reversing 5 and 20, which would make f decrease.