Given that the cost of an item increases by 2.5% each year.
Suppose that a jacket cost $100 in the year 2017.
Here,
![\begin{gathered} P=100 \\ r=0.025 \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/vea9ow572d5ll8vsxaiw.png)
Suppose after n years, the cost of the jacket will be $600.
Then,
![\begin{gathered} 600=100(1+0.025)^n \\ 6=(1.025)^n \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/xohsd77vq88zsb8hmopx.png)
Taking logarithm of both sides,
![\begin{gathered} \ln 6=n\ln (1.025) \\ n=(\ln 6)/(\ln (1.025)) \\ \approx72.6 \end{gathered}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/q4iizc5g16vopx9zp7uj.png)
By rounding to the nearest year, after 73 years the cost of the jacket will be $600.