Question

How to solve number 13

Answer 1

a) Each year the price increases by 3%, so if burger initially has price $p=\ 3.99$, then next year its price will be $1.03p\approx\ 4.11$. After another year, this price will increase by 3%, so that the burger would cost $1.03^2\approx\ 4.23$.

b) If the same pattern continues, then 10 years later we should expect the price to be $1.03^{10}p\approx\ 5.36$.

c and d) The pattern appears to be that the price $p$ of the burger after $t$ years, starting at a price $p_0$, is

$p(t)=1.03^tp_0$

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

$\ 20=1.03^t(\ 3.99)\implies t\approx54.5$

years later.