Answer to Question #208528 in Algebra for Manoj Soni

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)

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

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

$$0.02t=\ln1.1$$

$$t=50\ln1.1$$

$$t=4.7655\ years$$