1. **State the problem:** We need to solve for $n(t)$ in the equation: $$155000 = 17000 \left(1 + \frac{0.41}{12}\right)^{-n(t)}$$ 2. **Rewrite the equation:** Divide both sides by 17000 to isolate the exponential term: $$\frac{155000}{17000} = \left(1 + \frac{0.41}{12}\right)^{-n(t)}$$ 3. **Simplify the fraction:** $$\frac{155000}{17000} = \cancel{\frac{155000}{17000}} = 9.1176470588$$ 4. **Calculate the base inside the parentheses:** $$1 + \frac{0.41}{12} = 1 + 0.0341666667 = 1.0341666667$$ 5. **Rewrite the equation with simplified values:** $$9.1176470588 = (1.0341666667)^{-n(t)}$$ 6. **Take the natural logarithm of both sides:** $$\ln(9.1176470588) = \ln\left((1.0341666667)^{-n(t)}\right)$$ 7. **Use logarithm power rule:** $$\ln(9.1176470588) = -n(t) \cdot \ln(1.0341666667)$$ 8. **Solve for $n(t)$:** $$n(t) = -\frac{\ln(9.1176470588)}{\ln(1.0341666667)}$$ 9. **Calculate the logarithms:** $$\ln(9.1176470588) \approx 2.2103$$ $$\ln(1.0341666667) \approx 0.0336$$ 10. **Calculate $n(t)$:** $$n(t) = -\frac{2.2103}{0.0336} = -65.77$$ **Final answer:** $$n(t) \approx -65.77$$ This means the exponent $n(t)$ is approximately $-65.77$.