In exercise 100, you are given the dollar value of a product in 2005 and the rate at which the value of the product is expected to change during the next 5 years. Use this Info. to write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t=5 represent 2005.)
100.) 2005 value = $156
Rate: $4.50 increase per year
V = 4.50 (t-5) + Vi
where Vi is the initial 2005 value
To write a linear equation that gives the dollar value V of the product in terms of the year t, we need to find the rate of change of the product's value.
Given that we have the dollar value in 2005, which is $156, and we know that t = 5 represents 2005, we need to determine the rate of change for the next five years.
Let's assume that the rate of change is constant over the next five years. We can represent the rate of change as a decimal value, which we'll call r. We'll let t represent the number of years from 2005, so t = 0 will represent 2005 and t = 5 will represent 2010.
To calculate the value of the product in terms of the year t, we need to add the rate of change multiplied by the number of years to the initial value in 2005.
Therefore, the linear equation that gives the dollar value V of the product in terms of the year t can be written as:
V = 156 + r * t
In this equation, V represents the dollar value of the product and t represents the number of years from 2005. The rate of change, r, will be specific to the problem you are solving, and you will need to substitute the appropriate value for it.