Respuesta :
Answer:
8 years.
Explanation:
• The initial value of the laptop computer = $4700
,• Growth/Decay Rate = 75%=0.75
Thus, the value of the laptop after t years will be:
[tex]4700(0.75)^t[/tex]When the laptop is worth $600 or less:
[tex]4700(0.75)^t\leq600[/tex]We solve for t:
[tex]\begin{gathered} \text{Divide both sides by 4700} \\ \frac{4700(0.75)^t}{4700}=\frac{600}{4700} \\ (0.75)^t=\frac{600}{4,700} \\ \text{ Take the log:} \\ \log(0.75)^t=\log(\frac{600}{4,700}) \\ \text{ By the power law of logarithm:} \\ t\log(0.75)=\log(\frac{6}{47}) \\ \text{ Divide both sides by log 0.75} \\ t=\frac{\operatorname{\log}(\frac{6}{47})}{\operatorname{\log}(0.75)} \\ t=7.12 \end{gathered}[/tex]Thus, the computer be worth $600 or less after 8 years.
