Solve the equation $14.01 \times 1.08 ^ { t } = 52.76 \times 1.02 ^ { t }$
A) $t = 23.1$
B) $t = 645.83$
C) $t = 23.2$
D) $t = 23.69$

Question

Quizplus · Accepted Answer

To solve the equation, we can first simplify it by dividing both sides by $1.02^t$, giving us:

$$14.01 \cdot \left(\frac{1.08}{1.02}\right)^t = 52.76$$

Simplifying the fraction gives us:

$$14.01 \cdot 1.0588^t = 52.76$$

Dividing both sides by 14.01 gives us:

$$1.0588^t = 3.769$$

Taking the logarithm of both sides with base 1.0588 gives us:

$$t = \frac{\log(3.769)}{\log(1.0588)} \approx 23.2$$

Therefore, the best choice is C.

Solve the Equation 14.01×1.08t=52.76×1.02t14.01 \times 1.08 ^ { t } = 52.76 \times 1.02 ^ { t }14.01×1.08t=52.76×1.02t