Solve the equation $$14.24 \times 1.07 ^ { t } = 52.96 \times 1.03 ^ { t } .$$
A) $t = 34.06$
B) $t = 968$
C) $t = 34.47$
D) $t = 34.88$

Question

Quizplus · Accepted Answer

To solve the equation $14.24 \times 1.07^t = 52.96 \times 1.03^t$, we first divide both sides by $14.24$ to isolate the exponential terms on one side:$$1.07^t = \frac{52.96}{14.24} \times 1.03^t$$$$1.07^t = 3.72 \times 1.03^t$$Next, we divide both sides by $1.03^t$ to get:$$\left(\frac{1.07}{1.03}\right)^t = 3.72$$Taking the natural logarithm (ln) of both sides gives:$$t \cdot \ln\left(\frac{1.07}{1.03}\right) = \ln(3.72)$$Solving for $t$ gives:$$t = \frac{\ln(3.72)}{\ln\left(\frac{1.07}{1.03}\right)}$$Using a calculator:$$t \approx 34.47$$Therefore, the correct answer is $t = 34.47$.

Solve the Equation 14.24×1.07t=52.96×1.03t.14.24 \times 1.07 ^ { t } = 52.96 \times 1.03 ^ { t } .14.24×1.07t=52.96×1.03t.

Solve the Equation $14.24 \times 1.07 ^ { t } = 52.96 \times 1.03 ^ { t } .$