A nest of ants has been growing exponentially in such a way that its population, P, as a function of w weeks is given by P(w)=24, 000(1.063)^w Matthew claims that the population of ants is growing at a rate of 0.9% per day. Explain why Matthew’s claim is too high of a rate.

Asales representative from a local radio station is trying to convince the owner of a small fitness club to advertise on her station. the representative says that if the owner begins advertising on the station today, the club's total number of members will grow exponentially each month. she uses the given expression to model the number of club members, in hundreds, after advertising for t months.