Solve the exponential equation $24 = 2.27 \times 1.21 ^ { t }$ .
A) $t = 12.12$
B) $t = 17.96$
C) $t = 12.37$
D) $t = 13.04$

Question

Quizplus · Accepted Answer

First, divide both sides by 2.27 to isolate the exponent:

\begin{align*}
\frac{24}{2.27} &= 1.21^t \
10.57268723 &= 1.21^t
\end{align*}

Next, take the logarithm of both sides (any base can be used, but we will use the common logarithm):

\begin{align*}
\log(10.57268723) &= \log(1.21^t) \
1.023278986 &= t \cdot \log(1.21)
\end{align*}

Finally, divide by $\log(1.21)$:

\begin{align*}
t &= \frac{1.023278986}{\log(1.21)} \
t &\approx 12.37
\end{align*}

Therefore, the answer is choice C.

Solve the Exponential Equation 24=2.27×1.21t24 = 2.27 \times 1.21 ^ { t }24=2.27×1.21t