Advanced MathVery hardGrowth factor of an exponential from two values
Advanced Math practice question
The exponential function g satisfies g(0) = 4 and g(2) = 36, and g(x) is positive for every x. By what factor does g(x) grow each time x increases by 1?
Answer: 3
g(x) = 4·bˣ, so 4b² = 36 and b² = 9. Since g is positive, b = 3.
Common wrong answers
- If you answered 9
- 9 is b², the growth over two units, not one.
- If you answered 32
- 32 is g(2) − g(0), the total increase.
- If you answered 4.5
- 4.5 divides 36 by 4 by 2, treating the growth as linear.
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