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The expression
3(1.5)^(t) models the number of bacteria in a culture as a function of the number of hours since the culture was created.
What does 3 represent in this expression?
Choose 1 answer:
(A) There were initially 3 bacteria in the culture.
(B) The culture was created 3 hours ago.
(c) The number of bacteria is multiplied by 3 each hour.

The expression $3(1.5)^{t}$ models the number of bacteria in a culture as a function of the number of hours since the culture was created. $\newline$ What does $3$ represent in this expression? $\newline$ Choose $1$ answer: $\newline$ (A) There were initially $3$ bacteria in the culture. $\newline$ (B) The culture was created $3$ hours ago. $\newline$ (C) The number of bacteria is multiplied by $3$ each hour.

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Write exponential functions: word problems

Full solution

Q. The expression

3(1.5)^{t}

models the number of bacteria in a culture as a function of the number of hours since the culture was created.

\newline

What does

3

represent in this expression?

\newline

Choose

1

answer:

\newline

(A) There were initially

3

bacteria in the culture.

\newline

(B) The culture was created

3

hours ago.

\newline

(C) The number of bacteria is multiplied by

3

each hour.

Exponential function definition: The expression $3(1.5)^{t}$ is an exponential function where ' $t$ ' represents time in hours, and the base of the exponent, $1.5$ , represents the growth factor per hour. The number outside the parentheses, $3$ , is the initial amount before any growth has occurred.
Determining the initial amount: To understand what the number $3$ represents, we need to consider the value of the function when $t = 0$ , which is the starting point of the time measurement.
Substituting $t = 0$ : Substitute $t = 0$ into the expression to find the initial amount of bacteria. $\newline$ $3(1.5)^{(0)} = 3 \times 1 = 3$ $\newline$ Since any number raised to the power of $0$ is $1$ , the expression simplifies to just $3$ .
Interpreting the result: The result of the calculation shows that when $t = 0$ , the number of bacteria is $3$ . This indicates that the number $3$ represents the initial number of bacteria in the culture at the time it was created.

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