Answer:
and
.
Step-by-step explanation:
The equation can be simplified with the help of trigonometric identities:
Which means that equation is equal to zero if any component of the product is zero. The solutions of the expression are:
a)
b)
Any value different of both subsets do not satisfy the equation described above.
a) Each year the price increases by 3%, so if burger initially has price , then next year its price will be
. After another year, this price will increase by 3%, so that the burger would cost
.
b) If the same pattern continues, then 10 years later we should expect the price to be .
c and d) The pattern appears to be that the price of the burger after
years, starting at a price
, is
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
years later.
