Advanced MathMediumRewriting an exponential model with a different base
Advanced Math practice question
The function P is defined by P(t) = 500 · 4^(t/2). Which of the following is equal to P(t) for all t?
- A. 500 · 2ᵗCorrect
- B. 500 · 2^(t/2)
- C. 250 · 4ᵗ
- D. 500 · 8ᵗ
Answer: A. 500 · 2ᵗ
4^(t/2) = (4^(1/2))ᵗ = 2ᵗ, so P(t) = 500 · 2ᵗ.
Why the other answers are wrong
- B. 500 · 2^(t/2)
- 2^(t/2) = 4^(t/4), a slower growth.
- C. 250 · 4ᵗ
- Halving the coefficient does not change the base.
- D. 500 · 8ᵗ
- 8ᵗ grows far faster than 4^(t/2).
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