Question

The value, V (t), in dollars, of a stock t months after it is purchased is modeled by the following equation.

Answer 1

Answer:

Step-by-step explanation:$V(t)= 42(1-e ^{1.5t} ) +36$ is given value in dollars of a stock in t months after it is purchased.

a) Substitute 1 for t

$V(1) = 42(1-e^{-1.5} )+36 \\=67.852\\=67.85$

V(12) = $V(1) = 42(1-e^{-1.5*12} )+36 \\=77.00$

b) Find derivative for V

$V'(t) = 42(-1.5) e^{-1.5t} )\\\\=-63e^{-1.5t}$

c) When V(t) = 75

$V(t)=75= 42(1-e ^{1.5t} ) +36\\1-e ^{1.5t=0.9286\\=-2.639$

d) As t tends to infinity, exponent being in negative t tends to 0

So V tends to 42(1-0)+36 = 78