A copier purchased new for $4,800 depreciates in value $500 each year.
1. The function that models this equation is _
2. The rate of change for the function is _
3. The model predicts that the value of the copier after 3 years will be _
4. The model predicts that the value of the copier after 7 years will be _
1. The function that models this equation is V(t) = 4800 - 500t, where V(t) represents the value of the copier after t years.
2. The rate of change for the function is -500, which represents the decrease in value per year.
3. Plugging in t = 3 into the function, we have V(3) = 4800 - 500(3) = 4800 - 1500 = $3300. Therefore, the model predicts that the value of the copier after 3 years will be $3300.
4. Plugging in t = 7 into the function, we have V(7) = 4800 - 500(7) = 4800 - 3500 = $1300. Therefore, the model predicts that the value of the copier after 7 years will be $1300.
1. The function that models this equation is:
Cost = 4800 - 500n, where n is the number of years.
2. The rate of change for the function is -500, as indicated by the negative coefficient of n in the equation. This means that the value of the copier decreases by $500 every year.
3. To find the value of the copier after 3 years, we substitute n = 3 into the equation:
Cost = 4800 - 500(3) = 4800 - 1500 = $3300. Therefore, the model predicts that the value of the copier after 3 years will be $3300.
4. To find the value of the copier after 7 years, we substitute n = 7 into the equation:
Cost = 4800 - 500(7) = 4800 - 3500 = $1300. Therefore, the model predicts that the value of the copier after 7 years will be $1300.
1. The function that models this equation is a linear function. In general, the equation for a linear function is y = mx + b, where y represents the dependent variable (in this case, the value of the copier), x represents the independent variable (the number of years), m represents the rate of change, and b represents the initial value.
In this specific case, the initial value is $4,800, and the rate of change is -$500 (since the value of the copier decreases by $500 each year). Therefore, the equation that models this situation would be y = -500x + 4800.
2. The rate of change for the function is -500. This means that for every increase of one year, the value of the copier decreases by $500.
3. To find the value of the copier after 3 years using the model, simply substitute x = 3 into the equation:
y = -500(3) + 4800
y = -1500 + 4800
y = 3300
According to the model, the value of the copier after 3 years will be $3300.
4. To find the value of the copier after 7 years using the model, substitute x = 7 into the equation:
y = -500(7) + 4800
y = -3500 + 4800
y = 1300
According to the model, the value of the copier after 7 years will be $1300.