The value of a baseball card in dollars has been found to be 0.15y + 0.35, where y is the number of years since it was released. By how much is the baseball card's value increasing per year?
AAAaannndd the bot gets it wrong yet again!
the slope of the line is 0.15 -- the rate of change
Good grief :(
To find the amount by which the baseball card's value is increasing per year, we need to determine the derivative of the given equation with respect to time (in this case, represented by the number of years, y).
The derivative of 0.15y is 0.15, since when we differentiate y with respect to y, we get 1.
The derivative of 0.35 is 0, as 0.35 is a constant and its derivative is zero.
So, taking the derivative of the given equation:
dV/dy = d(0.15y + 0.35)/dy
= d(0.15y)/dy + d(0.35)/dy
= 0.15 + 0
= 0.15
Therefore, the baseball card's value is increasing by 0.15 dollars per year.