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The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour. There were initially 500 bacteria.
Which expression gives the number of bacteria after 3 hours?
Choose 1 answer:
(A)
500+1.2*1.2*1.2
(B)
500*1.2*1.2*1.2
(C)
500+1.2+1.2+1.2
(D)
500*(1.2+1.2+1.2)

The number of bacteria in a petri dish is multiplied by a factor of $1$ . $2$ every hour. There were initially $500$ bacteria. $\newline$ Which expression gives the number of bacteria after $3$ hours? $\newline$ Choose $1$ answer: $\newline$ (A) $500+1.2 \cdot 1.2 \cdot 1.2$ $\newline$ (B) $500 \cdot 1.2 \cdot 1.2 \cdot 1.2$ $\newline$ (C) $500+1.2+1.2+1.2$ $\newline$ (D) $500 \cdot(1.2+1.2+1.2)$

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Write exponential functions: word problems

Full solution

Q. The number of bacteria in a petri dish is multiplied by a factor of

1

.

2

every hour. There were initially

500

bacteria.

\newline

Which expression gives the number of bacteria after

3

hours?

\newline

Choose

1

answer:

\newline

(A)

500+1.2 \cdot 1.2 \cdot 1.2

\newline

(B)

500 \cdot 1.2 \cdot 1.2 \cdot 1.2

\newline

(C)

500+1.2+1.2+1.2

\newline

(D)

500 \cdot(1.2+1.2+1.2)

Identify initial data: Identify the initial number of bacteria and the growth factor per hour. $\newline$ Initial number of bacteria = $500$ $\newline$ Growth factor per hour = $1.2$
Understand exponential growth: Understand that the growth of bacteria is exponential, meaning the bacteria are multiplied by the growth factor every hour.
Calculate after $1$ hour: Calculate the number of bacteria after $1$ hour. $\newline$ After $1$ hour: $500 \times 1.2$
Calculate after $2$ hours: Calculate the number of bacteria after $2$ hours. $\newline$ After $2$ hours: $(500 \times 1.2) \times 1.2 = 500 \times (1.2)^2$
Calculate after $3$ hours: Calculate the number of bacteria after $3$ hours. $\newline$ After $3$ hours: $500 \times (1.2)^2$ \times $1$ . $2$ = $500 \times (1.2)^3$
Identify correct expression: Identify the correct expression from the given options that matches the calculation for the number of bacteria after $3$ hours. $\newline$ The correct expression is (B) $500 \times 1.2 \times 1.2 \times 1.2$

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