Answer to Question #318981 in Calculus for sarah

Question

If the net investment function is given by I (t) = 100e^ {0.1t} calculate

(a) The capital formation from the end of the second year to the end of the fifth year;

(b) The number of years required before the capital stock exceeds $100 000

Answer 1

(a) we have to calculate:

$I(5) - I(2) = 100 e^{0.1*5} - 100 e^{0.1*2} = 100(1.649 - 1.221)=42.8$

(b)

$I(t) = 100000\\ 100 e^{0.1*t} = 100 000\\ e^{0.1*t} = 1000 | ln(.)\\ 0.1*t = 6.908\\ t = 69.08$