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I am looking over at some math questions and I encountered this problem:

The growth of a certain organism can be modeled by $$C(t) = 10(1.029)^{24t},$$ where $C(t)$ is the total number of cells after $t$ hours. Which function is approximately equivalent to $C(t)$?
(1) $C(t) = 240(.083)^{24t}$
(2) $C(t) = 10(.083)^t$
(3) $C(t) = 10(1.986)^t$
(4) $C(t) = 240(1.986)^{t/24}$

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The answer to this problem is (3) and this is an exponential model. The way I would approach this problem is substitute some values for t and see which values are closer to the given equation. However, I'm posting this question to see if there is alternate ways to solve this problem since my way would take quite some time.

Em.
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Justin
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    (1) and (2) cannot possibly be the answer since they both represent exponential decay (that common ratio is $< 1$). (4) cannot possibly be correct because it doesn't have the correct initial value. Ultimately it should be clear that (3) is correct because $1.029^{24t} = (1.029^{24})^t \approx 1.985\ 953\ 128\ 62^t$. – Jared Jul 16 '16 at 06:48
  • Formatting tips here. – Em. Jul 16 '16 at 06:57

1 Answers1

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Hint. One may observe that $$ 1.029^{\color{red}{24}t}=\left(1.029^{\color{red}{24}}\right)^t\approx\left(1.986\right)^t. $$

Olivier Oloa
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