Question
Suppose a bacterial culture triples in population every 5 hours. If the population is initially 200 ,
(a) quickly determine when the population will reach 5400 .
(b) Find an equation for the population at any time.
(c) Determine when the population will reach 20,000 .

Answer

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$Final Answer:$ $a)$ 15 hours, $b)$ $P (t) = 200 * ({1.24573}^{t})$ , $c)$ 20.96 hours

Steps

Step 1 ：Use the exponential growth formula: $P (t) = P_{0} * (r^{t})$ , where $P (t)$ is the population at time $t$ , $P_{0}$ is the initial population, $r$ is the growth rate, and $t$ is the time.

Step 2 ：Calculate the growth rate: $r = 3^{(1 / 5)} = 1.24573$

Step 3 ： $a)$ Find when the population reaches 5400: $5400 = 200 * ({1.24573}^{t})$ , solving for $t$ , we get $t \approx 15$ hours.

Step 4 ： $b)$ The equation for the population at any time is: $P (t) = 200 * ({1.24573}^{t})$

Step 5 ： $c)$ Find when the population reaches 20000: $20000 = 200 * ({1.24573}^{t})$ , solving for $t$ , we get $t \approx 20.96$ hours.

Step 6 ： $Final Answer:$ $a)$ 15 hours, $b)$ $P (t) = 200 * ({1.24573}^{t})$ , $c)$ 20.96 hours

QuestionSuppose a bacterial culture triples in population every 5 hours. If the population is initially 200 ,(a) quickly determine when the population will reach 5400 .(b) Find an equation for the population at any time.(c) Determine when the population will reach 20,000 .

Answer

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Question
Suppose a bacterial culture triples in population every 5 hours. If the population is initially 200 ,
(a) quickly determine when the population will reach 5400 .
(b) Find an equation for the population at any time.
(c) Determine when the population will reach 20,000 .