what is the estimated amount for vet bills?

Question

the annual amount spent in the United States on veterinary bills rfor dogs, m(t), in billions of dollars, can be estimated by the function m(t)=0.05t^2 - 1.5t+ 1.2, use the function to estimate the amount spent on veterinary bills for dogs in 2003.

in what year will $25 billion be spent on vet. bills for their dogs?

Answer 1

Just plug in 25Bfor the total, and solve for t (you don't have to plug in 25,000,000,000 since the problem said that the answer is already in billions):

m(t) = 0.05t^2 - 1.5t + 1.2
25 = 0.05t^2 - 1.5t + 1.2
0 = 0.05t^2 - 1.5t - 23.8

Now use the quadratic equation:
t = [-b +/- sqrt(b^2 - 4ac)] / 2a
t = [1.5 +/- sqrt((-1.5)^2 - 4(0.05)(-23.8))] / 2(0.05)
t = [1.5 +/- sqrt(2.25 + 4.76)] / 0.1
t = [1.5 +/- sqrt(7.01)] / 0.1
t = [1.5 +/- 2.648] / 0.1
t = 41.646, -11.476

Since we can't go backwards in time, in just over 41 years we will have spent $25B on vet care.