Solve the equation $14.84 \times 1.08 ^ { t } = 52.89 \times 1.02 ^ { t }$
A) $t = 21.77$
B) $t = 634.17$
C) $t = 22.23$
D) $t = 22.97$

Question

Quizplus · Accepted Answer

Starting with the given equation:
$$14.84 \times 1.08 ^ { t } = 52.89 \times 1.02 ^ { t }$$

Step 1: Divide both sides by $1.02^t$ to get:
$$14.84 \times \left( \frac{1.08}{1.02} \right) ^ t = 52.89$$

Step 2: Simplify the term in parentheses:
$$14.84 \times 1.0588 ^ t = 52.89$$

Step 3: Divide both sides by 14.84 to get:
$$1.0588^t = \frac{52.89}{14.84} \approx 3.56$$

Step 4: Take the natural logarithm of both sides to solve for t:
$$\ln (1.0588^t) = \ln 3.56$$
$$t \ln 1.0588 = \ln 3.56$$
$$t = \frac{\ln 3.56}{\ln 1.0588} \approx 22.23$$

Therefore, the best choice is C.

Solve the Equation 14.84×1.08t=52.89×1.02t14.84 \times 1.08 ^ { t } = 52.89 \times 1.02 ^ { t }14.84×1.08t=52.89×1.02t

Solve the Equation $14.84 \times 1.08 ^ { t } = 52.89 \times 1.02 ^ { t }$