Every year, Sam will have 103% of the amount from the previous year.
[tex]p\%=\dfrac{p}{100}\\\\103\%=\dfrac{103}{100}=1.03[/tex]
After the first year:
[tex]1.03\cdot\$4,500[/tex]
After the second year:
[tex]1.03\cdot1.03\cdot\$4,500=\$4,500(1.03)^2[/tex]
After the t-th year:
[tex]\$4,500(1.03)^t[/tex]
Therefore we have the inequality:
[tex]\$4,500(1.03)^t\leq\$7,020\ \ \ \ |\text{divide both sides by \$4,500}\\\\(1.03)^t\leq1.56\\\\(1.03)^{15}\approx15.56\\\\\text{therefore}\ t\leq15[/tex]
Answer: t ≤ 15.
