the salvage value s (in dollars) of a company limosine after t years is estimated to be given by the formula…

the salvage value s (in dollars) of a company limosine after t years is estimated to be given by the formula below. use the formula to answer the questions. s(t)=600,000(0.8)^t what is the rate of depreciation (in dollars per year) after 1 year? $ - 107,108.90 per year (do not round until the final answer. then round to the nearest cent as needed.) what is the rate of depreciation (in dollars per year) after 5 years? $ - 43,871.81 per year (do not round until the final answer. then round to the nearest cent as needed.) what is the rate of depreciation (in dollars per year) after 10 years? $ per year (do not round until the final answer. then round to the nearest cent as needed.)

the salvage value s (in dollars) of a company limosine after t years is estimated to be given by the formula below. use the formula to answer the questions. s(t)=600,000(0.8)^t what is the rate of depreciation (in dollars per year) after 1 year? $ - 107,108.90 per year (do not round until the final answer. then round to the nearest cent as needed.) what is the rate of depreciation (in dollars per year) after 5 years? $ - 43,871.81 per year (do not round until the final answer. then round to the nearest cent as needed.) what is the rate of depreciation (in dollars per year) after 10 years? $ per year (do not round until the final answer. then round to the nearest cent as needed.)

Answer

Explanation:

Step1: Find the derivative of $S(t)$

The function $S(t)=600000(0.8)^t$. Using the formula for the derivative of an exponential function $y = a\cdot b^x$ which is $y^\prime=a\cdot b^x\ln(b)$, we have $S^\prime(t)=600000(0.8)^t\ln(0.8)$.

Step2: Evaluate $S^\prime(t)$ at $t = 10$

Substitute $t = 10$ into $S^\prime(t)$. So $S^\prime(10)=600000(0.8)^{10}\ln(0.8)$. First, calculate $(0.8)^{10}=0.1073741824$. Then $\ln(0.8)\approx - 0.2231435513$. $S^\prime(10)=600000\times0.1073741824\times(- 0.2231435513)$. $S^\prime(10)=600000\times(-0.0239682777)\approx - 14380.97$.

Answer:

$-14380.97$