Respuesta :
The general exponential decay formula is:
[tex]\begin{gathered} y=a\cdot b^x \\ \text{with b < 1} \end{gathered}[/tex]In this case, y represents the value of the car and x represents time. At x = 0, y = 41000 (initial value), then:
[tex]\begin{gathered} 41000=a\cdot b^0^{} \\ 41000=a \end{gathered}[/tex]At x = 4, y = 41000/2, then:
[tex]\begin{gathered} \frac{41000}{2}=41000\cdot b^4 \\ \frac{1}{2}=b^4 \\ \log _{10}(\frac{1}{2})=4\log _{10}b \\ -\frac{0.301}{4}=\log _{10}b \\ 10^{-0.07525}=b \\ 0.841=b \end{gathered}[/tex]At x = 6,
[tex]\begin{gathered} y=41000\cdot0.841^6 \\ y=41000\cdot0.3538 \\ y=14500 \end{gathered}[/tex]The value of the car is $14500 after 6 years
