Solve the problem.
-The interest I earned in $1 \mathrm{yr}$ on a fixed principal varies directly as the interest rate $\mathrm{r}$. An investment earns $\$ 25.38$ at an interest rate of $3.55 \%$. Find an equation of variation.
A) $\mathrm{I}=-\frac{355}{2538} \mathrm{r}$
B) $\mathrm{I}=\frac{2183}{100} \mathrm{r}$
C) $\mathrm{I}=\frac{2538}{355} \mathrm{r}$
D) $\mathrm{I}=\frac{355}{2538} \mathrm{r}$

Question

Quizplus · Accepted Answer

The equation of variation is $I = k \cdot r$, where $k$ is the constant of variation. To find $k$, use the given information: $I = 25.38$ when $r = 3.55\%$. Convert $3.55\%$ to a decimal by dividing by 100, giving $r = 0.0355$. Solve for $k$ by rearranging the equation to $k = \frac{I}{r} = \frac{25.38}{0.0355} = \frac{2538}{355}$. Thus, the equation of variation is $I = \frac{2538}{355}r$.

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