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P(t)=30(2)^((t)/( 18))
The function models
P, the amount of bacteria, in colony-forming units, in a bacteria culture after
t minutes of growth. How many colonyforming units of bacteria are in the bacteria culture after 90 minutes?
Choose 1 answer:
(A)
3×10^(2)
(B)
9.6 ×10^(2)
(c)
5.4 ×10^(3)
(D)
2.43 ×10^(7)

$P(t)=30(2)^{\frac{t}{18}}$ $\newline$ The function models $P$ , the amount of bacteria, in colony-forming units, in a bacteria culture after $t$ minutes of growth. How many colonyforming units of bacteria are in the bacteria culture after $90$ minutes? $\newline$ Choose $1$ answer: $\newline$ (A) $3 \times 10^{2}$ $\newline$ (B) $9.6 \times 10^{2}$ $\newline$ (C) $5.4 \times 10^{3}$ $\newline$ (D) $2.43 \times 10^{7}$

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Compare linear and exponential growth

Full solution

Q.

P(t)=30(2)^{\frac{t}{18}}

\newline

The function models

P

, the amount of bacteria, in colony-forming units, in a bacteria culture after

t

minutes of growth. How many colonyforming units of bacteria are in the bacteria culture after

90

minutes?

\newline

Choose

1

answer:

\newline

(A)

3 \times 10^{2}

\newline

(B)

9.6 \times 10^{2}

\newline

(C)

5.4 \times 10^{3}

\newline

(D)

2.43 \times 10^{7}

Identify function and time: Identify the given function and the time at which we need to find the amount of bacteria. $\newline$ The function given is $P(t) = 30(2)^{\frac{t}{18}}$ , where $P$ is the amount of bacteria and $t$ is the time in minutes. $\newline$ We need to find $P(90)$ , the amount of bacteria after $90$ minutes.
Substitute value and calculate: Substitute the value of $t$ with $90$ in the function to calculate the amount of bacteria. $P(90) = 30(2)^{\frac{90}{18}}$
Simplify exponent: Simplify the exponent by dividing $90$ by $18$ . $\newline$ $\frac{90}{18} = 5$ $\newline$ So, $P(90) = 30(2)^5$
Calculate $2$ to the power of $5$ : Calculate $2$ raised to the power of $5$ . $\newline$ $2^5 = 32$
Multiply result by $30$ : Multiply the result from Step $4$ by $30$ to find the amount of bacteria after $90$ minutes. $\newline$ $P(90) = 30 \times 32$ $\newline$ $P(90) = 960$
Convert to scientific notation: Convert the result to scientific notation if necessary. $\newline$ $960$ can be written as $9.6 \times 10^2$ in scientific notation.
Choose correct answer: Choose the correct answer from the given choices. $\newline$ The correct answer is (B) $9.6 \times 10^2$ .

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