Question

the company bought $15000 worth of equipment beginnning of year 2018 the equipment is est. to increase in value at a rate of 15.9% per year how many yers, t , after which the value of the company's new equipment will be less than 7500 what formula would be used

Answer 1

To solve this problem, we can use the formula for exponential growth:

V(t) = V0 * (1 + r)^t

where:

V(t) is the value of the equipment at time t

V0 is the initial value of the equipment ($15,000)

r is the annual growth rate (15.9% or 0.159)

t is the time in years

We want to find the time t when the value of the equipment will be less than $7500. So we can set up the following inequality:

V(t) < 7500

Substituting the formula for V(t), we get:

V0 * (1 + r)^t < 7500

Substituting the given values, we get:

15000 * (1 + 0.159)^t < 7500

Simplifying and solving for t,

we get:(1 + 0.159)^t < 0.5

t * log(1 + 0.159) < log(0.5)

t > log(0.5) / log(1 + 0.159)

Using a calculator, we get:

t > 2.64

So the company's new equipment will be worth less than $7500 after about 2.64 years.

Explanation: