QuestionFind the solution of the exponential equation $$100(1.04)^{2 t}=500,000$$ in terms of logarithms, or correct to four decimal places. $$t=$$ $\square$ Quest $\square$ Funcs Trig $\square$ $x_{\square}$ $\sqrt{ }$ $\sqrt[n]{ }$ $\square$ $\uparrow$ 1

Studdy Solution
Solve for $t$ by dividing both sides by $2 \cdot \ln(1.04)$:
$$2t = \frac{\ln(5,000)}{\ln(1.04)}$$ $$t = \frac{\ln(5,000)}{2 \cdot \ln(1.04)}$$
Calculate the value of $t$ to four decimal places:
$$t \approx \frac{\ln(5,000)}{2 \cdot \ln(1.04)} \approx \frac{8.5172}{0.0781} \approx 54.5932$$
The value of $t$ is approximately:
$$\boxed{54.5932}$$