a) Each year the price increases by 3%, so if burger initially has price [tex]p=\$3.99[/tex], then next year its price will be [tex]1.03p\approx\$4.11[/tex]. After another year, this price will increase by 3%, so that the burger would cost [tex]1.03^2\approx\$4.23[/tex].
b) If the same pattern continues, then 10 years later we should expect the price to be [tex]1.03^{10}p\approx\$5.36[/tex].
c and d) The pattern appears to be that the price [tex]p[/tex] of the burger after [tex]t[/tex] years, starting at a price [tex]p_0[/tex], is
[tex]p(t)=1.03^tp_0[/tex]
which forms a geometric sequence that diverges. This necessarily means that the price would eventually exceed $20, and we find that that time comes about
[tex]\$20=1.03^t(\$3.99)\implies t\approx54.5[/tex]
years later.
