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.