. The value of a lottery prize doubles each week until there is a winner. If
the prize is $1000 the first week,
write a recursive function rule and an
explicit function rule to model the
value of the prize P, in dollars, after t
weeks without a winner. (14.2)

P(t) = $1000*2^t

Step-by-step explanation:

Ok, we know that in the week 1 the price is: p = $1000

After one week, the price doubles, so here we have: p = 2*$1000

After another week, the price doubles again, here the price is:

p = 2*(2*$1000) = $1000*2^2

Here we already can see the relation, for each week, we multiply the previous price by two, which will increase the exponent in the two by 1 unit.

Then, for week number t, the price will be:

P(t) = $1000*2^t