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Which equation describes the story below? You have
$5 and triple your money every day.
a
y=15 x
b
y=5(3x)
c
y=5(3)^(x)
d
y=5^(x)
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Which equation describes the story below? You have $\$ 5$ and triple your money every day. $\newline$ a) $y=15 x$ $\newline$ b) $y=5(3 x)$ $\newline$ c) $y=5(3)^{x}$ $\newline$ d) $y=5^{x}$

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Find the number of solutions

Full solution

Q. Which equation describes the story below? You have

\$ 5

and triple your money every day.

\newline

a)

y=15 x

\newline

b)

y=5(3 x)

\newline

c)

y=5(3)^{x}

\newline

d)

y=5^{x}

Identify initial amount and rate: Identify the initial amount of money and the rate of increase. The story starts with $\$5$ and the money triples every day. This means the initial amount is $\$5$ and the rate of increase is a multiplication by $3$ each day.
Determine mathematical representation: Determine the mathematical representation of the rate of increase. $\newline$ Tripling your money every day can be represented by raising $3$ to the power of $x$ , where $x$ is the number of days. This is because each day, the money is multiplied by $3$ .
Combine initial amount and rate: Combine the initial amount with the rate of increase to form an equation. $\newline$ The initial amount is $\$5$ , and it needs to be multiplied by the rate of increase, which is $3$ raised to the power of $x$ . The equation that represents this situation is $y = 5 \times 3^x$ .
Match equation with choices: Match the equation with the given choices. $\newline$ The equation we have found is $y = 5 \times 3^x$ . This matches with choice (c) $y = 5(3)^x$ .

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