1) a 2019 chevy silverodo used by a local business to make deliveries originally cost $68,000 depreciates at…

Explanation:

Step1: Set up the depreciation formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $A$ is the final value, $P$ is the initial value, $r$ is the rate of depreciation, and $t$ is the number of years. We know that $P=$68000$, $r = 0.0735$, and we want $A=\frac{P}{2}$. Substituting these values into the formula, we get $\frac{P}{2}=P(1 - 0.0735)^t$.

Step2: Simplify the equation

Divide both sides of the equation $\frac{P}{2}=P(0.9265)^t$ by $P$ (since $P\neq0$). We obtain $\frac{1}{2}=(0.9265)^t$.

Step3: Take the natural logarithm of both sides

$\ln(\frac{1}{2})=\ln(0.9265^t)$. Using the property of logarithms $\ln(a^b)=b\ln(a)$, we can rewrite the right - hand side as $t\ln(0.9265)$. So, $\ln(\frac{1}{2}) = t\ln(0.9265)$.

Step4: Solve for $t$

$t=\frac{\ln(\frac{1}{2})}{\ln(0.9265)}$. We know that $\ln(\frac{1}{2})=-\ln(2)\approx - 0.6931$ and $\ln(0.9265)\approx-0.0767$. Then $t=\frac{- 0.6931}{-0.0767}\approx9$.

Answer:

9 years