Solve the equation $14.57 \times 1.06 ^ { t } = 52.17 \times 1.02 ^ { t }$
A) $t = 32.19$
B) $t = 940$
C) $t = 33.16$
D) $t = 33.93$

Name: Solve the equation $14.57 \times 1.06 ^ { t } = 52.17 \times 1.02 ^ { t }$ A) $t = 32.19$ B) $t = 940$ C) $t = 33.16$ D) $t = 33.93$
Brand: Quizplus
Rating: 4.8 (34 reviews)

Question

Quizplus · Accepted Answer

Dividing both sides by $1.02^t$ and then simplifying gives us:
$$\frac{14.57}{52.17} = \left(\frac{1.02}{1.06}\right)^t$$
$$0.2788 = 0.9623^t$$
$$t = \frac{\ln 0.2788}{\ln 0.9623} \approx 33.16$$
Therefore, the best choice is C.

Solve the Equation 14.57×1.06t=52.17×1.02t14.57 \times 1.06 ^ { t } = 52.17 \times 1.02 ^ { t }14.57×1.06t=52.17×1.02t

Solve the Equation $14.57 \times 1.06 ^ { t } = 52.17 \times 1.02 ^ { t }$