Answer:
A) 2.9% of GDP
B) 8.73% of GDP
Step-by-step explanation:
A) To find the rate of spending, let's find the derivative of the function
P(t) = 0.27t² + 1.4t + 2.1 (0 <= t <= 5)
So,
dP/dt = 0.54t + 1.4 which is the annual growth rate.
Since t is measured in decades, thus in 2030 ,it will have been 3 decades, so we have t = 3
So, at t=3; dp/dt = 0.5(3) + 1.4 = 1.5 + 1.4 = 2.9 which means spending in 2030 will be growing at rate of 2.9%
B) The predicated spending is;
P(t) = 0.27t² + 1.4t + 2.1
Thus, in 2030, will be 3 decades so, t= 3
Thus;
P(3) = 0.27(3²) + 1.4(3) + 2.1 = 8.73 which is 8.73% of GDP
