You are given the dollar value of a product in 2015 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 15 represent 2015.)
2015 Value: $245,000
Rate:$5200 decrease per year
since the value decreases 5200 each year,
v = 245000 - 5200(t-15) for 15 <= t <= 20
Well, well, well, looks like we have a mathematical challenge on our hands! Don't worry, I'm here to help. Let's clown around with some numbers.
To come up with a linear equation that represents the dollar value V of the product in terms of the year t, we need to determine the starting point in 2015 and the rate at which the value is expected to change per year.
Given that the value in 2015 is $245,000 and the rate of decrease is $5200 per year, we can set up our equation like this:
V = 245,000 - 5200(t - 15)
Now, let's break it down. (t - 15) represents the number of years after 2015. Since we want the value to decrease by $5200 per year, we multiply that rate by (t - 15). Finally, we subtract that value from the starting value of $245,000.
So, the linear equation for the dollar value V of the product in terms of the year t is:
V = 245,000 - 5200(t - 15)
Hope this equation puts a smile on your face while dealing with numbers!
To write a linear equation that gives the dollar value V of the product in terms of the year t, we can use the slope-intercept form of a linear equation, which is given by:
V = mt + b
where m is the slope (rate of change) and b is the y-intercept (the value in the starting year).
In this case, we know that the starting year is 2015 (represented by t = 15) and the rate of change is a $5200 decrease per year. Therefore, the slope is -5200 and the y-intercept is the starting value of $245,000.
Substituting these values into the equation, we get:
V = -5200t + 245,000
This is the linear equation that gives the dollar value V of the product in terms of the year t.
To write a linear equation that gives the dollar value V of the product in terms of the year t, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the initial value in 2015 is $245,000, and the value is expected to decrease by $5,200 every year. So, the slope (m) would be -5200 (negative because it represents a decrease) and the initial value in 2015 would be the y-intercept (b).
Therefore, the equation that relates the year t to the dollar value V would be:
V = -5200t + 245000
Here, t represents the number of years after 2015. So, for example, if you want to find the value of the product in 2020 (5 years after 2015), you would substitute t = 5 into the equation:
V = -5200(5) + 245000
V = -26000 + 245000
V = $219,000
So, the dollar value of the product in 2020 would be $219,000.