Question

The dollar value of a product in 2015 and the rate at which the value of the product is expected to change over the next 5 years. Formulate a linear equation expressing the dollar value (V) of the product in terms of the year (t), with t = 15t=15 representing the year 2015. The given information is as follows:

a. 2015 Value: $179
b. Rate: $4.50 increase per year

Answer 1

The linear equation expressing the dollar value (V) of a product in terms of the year (t) is V = 4.50(t - 15) + 179, with t = 15 representing the year 2015 and accounting for a $4.50 increase in value per year starting from a base value of $179.

Step-by-step explanation:

To formulate a linear equation expressing the dollar value (V) of the product in terms of the year (t), we start with the given information: the product's value in 2015 ($179) and the rate of increase ($4.50 per year). Since we are denoting the year 2015 as t = 15, our base year for t will be 2015, making each incremental unit of t equivalent to one year. The linear equation will thus take the form of V = mt + b, where m is the rate of change per year and b is the initial value when t = 15.

Substituting the given values into the equation, we get:

V = 4.50(t - 15) + 179,
Solving for V when t=15 (year 2015):
V = 4.50(15 - 15) + 179
V = 179

This equation now shows the expected future value of the product for any year after 2015 by simply plugging the corresponding value of t (where t = the year - 2000).