Question

A toy tractor sold for $274 in 1979 and was sold again in 1990 for $426. Assume that the growth in the value V of the

collector's item was exponential.
a) Find the value k of the exponential growth rate. Assume V = 274.
k=
(Round to the nearest thousandth.)

Answer 1

To find the value of k, the exponential growth rate, we can use the formula for exponential growth: V = V0e^(kt). Given the initial value, V0, and the time elapsed, t, we can substitute these values into the equation to solve for k. In this case, the value of k is 0.

Step-by-step explanation:

To find the value of k, the exponential growth rate, we can use the formula for exponential growth:

V = V0e^(kt)

Given that V = 274 (the initial value), V0 = 274, and t = 1990 - 1979 = 11 (the time elapsed), we can substitute these values into the equation to solve for k.

274 = 274e^(11k)

Divide both sides of the equation by 274:

1 = e^(11k)

Take the natural logarithm of both sides to isolate k:

ln(1) = ln(e^(11k))

0 = 11k

Divide both sides of the equation by 11:

0 = k

Therefore, the value of k is 0.