Solve the exponential equation $22 = 2.43 \times 1.21 ^ { t }$
A) $t = 11.5$
B) $t = 16.17$
C) $t = 11.56$
D) $t = 12.06$

Question

Quizplus · Accepted Answer

Start by dividing both sides by 2.43 to isolate the exponential term:

$$\frac{22}{2.43} = 1.21^t$$

Use a calculator to evaluate the left-hand side:

$$\frac{22}{2.43} \approx 9.04938$$

Take the logarithm of both sides (with any base you like):

$$\log(9.04938) = t \log(1.21)$$

Divide by $\log(1.21)$ to solve for $t$:

$$t = \frac{\log(9.04938)}{\log(1.21)} \approx 11.56$$

Therefore, the best choice is C, with an answer of $t = 11.56$.

Solve the Exponential Equation 22=2.43×1.21t22 = 2.43 \times 1.21 ^ { t }22=2.43×1.21t