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The expression
4*3^(t) gives the number of ducks living in Anoop's pond
t years after he built it.
What does 4 represent in this expression?
Choose 1 answer:
(A) It has been 4 years since Anoop built the pond.
(B) The number of ducks living in Anoop's pond is multiplied by 4 every year.
(c) There were 4 ducks living in Anoop's pond when he first built it.

The expression $4 \cdot 3^{t}$ gives the number of ducks living in Anoop's pond $t$ years after he built it. $\newline$ What does $4$ represent in this expression? $\newline$ Choose $1$ answer: $\newline$ (A) It has been $4$ years since Anoop built the pond. $\newline$ (B) The number of ducks living in Anoop's pond is multiplied by $4$ every year. $\newline$ (C) There were $4$ ducks living in Anoop's pond when he first built it.

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Write exponential functions: word problems

Full solution

Q. The expression

4 \cdot 3^{t}

gives the number of ducks living in Anoop's pond

t

years after he built it.

\newline

What does

4

represent in this expression?

\newline

Choose

1

answer:

\newline

(A) It has been

4

years since Anoop built the pond.

\newline

(B) The number of ducks living in Anoop's pond is multiplied by

4

every year.

\newline

(C) There were

4

ducks living in Anoop's pond when he first built it.

Exponential function definition: The expression $4 \cdot 3^{t}$ is an exponential function where $t$ is the exponent and represents the number of years after Anoop built the pond. To understand what the number $4$ represents, we need to consider the value of the expression when $t = 0$ , which is the time Anoop built the pond.
Substituting $t = 0$ : Substitute $t = 0$ into the expression to find the initial number of ducks. The expression becomes $4 \cdot 3^{0}$ . Since any number raised to the power of $0$ is $1$ , we have $3^{0} = 1$ .
Calculating the initial number of ducks: Now, calculate the number of ducks when $t = 0$ . The expression simplifies to $4 \times 1$ , which equals $4$ . This means that when Anoop first built the pond, there were $4$ ducks in it.
Interpreting the meaning of $4$ : Based on the calculation, the number $4$ in the expression $4 \cdot 3^{t}$ represents the initial number of ducks in Anoop's pond when he first built it. Therefore, the correct answer is (C) There were $4$ ducks living in Anoop's pond when he first built it.

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