Question

An economy is forecasted to grow continuously so that the gross national product (GNP), measured in billions of dollars, after ‘t’ years is given as

GNP = 80.e^0.02t

(a)   Calculate the current GNP and the GNP in the three years’ time.

(b)In how many years is GNP forecasted to be $88 billion

Answer 1

(a)

$$GNP(0)=\$80\ billion$$

$$GNP(3)=80e^{0.02(3)}$$

$$GNP(3)=\$84.947\ billion$$

(b)

$$GNP(t)=80e^{0.02t}=88$$

$$e^{0.02t}=1.1$$

$$0.02t=\ln1.1$$

$$t=50\ln1.1$$

$$t=4.7655\ years$$