Question

The initial value of a stock is $2500. The value of the stock is expected to grow at an annual rate of 4%. Let x represent the number of years since the stock was made available for purchase. Let y represent the value of the stock x years later. What equation models the value of the stock x years after it was made available?

Answer 1

Explanation:

Initial value of the stock is $2500 This means that the principal is

P = 2500

The value of the stock is expected to grow at an annual rate. This means that it grew once in a year. So

n = 1

The rate at which the stock grew is 4%. So

r = 4/100 = 0.04

x represent the number of years since the stock was made available for purchase.. So

t = x

The formula for determining the value of the stock x years later would be

A = P(1+r/n)^nt

A = total value of the stock x years later. Let y represent the value of the stock x years later. Therefore,

y = 2500 (1+0.04/1)^1×x

y = 2500(1.04)^x

Answer 2

y = ($2500)(1.04)^x

Explanation:

The initial value = $2500

The value of the stock is expected to grow at the rate of 4%

Let x represent the number of years since the stock was made available for purchase.

Let y represent the value of the stock x years later.

y1 = amount of money after one year.

y1 = $2500 (100% + 4%)

y1 = $2500 (104%)

y1 = $2500(1.04)

y2 = amount of money after two years

y2 = y1 (100% + 4%)

y2 = y1 (104%)

y2 = y1(1.04)

y2 = $2500(1.04)(1.04)

y2 = $2500(1.04)^2

This will give a pattern

y5 = $2500(1.04)^5

After x years the model of the equation will be y = ($2500)(1.04)^x