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Interpreting linear functions — Basic example

Video transcript

the amount of money that farmers in Massachusetts paid to maintain their crops between 1991 and 2008 is modeled by the equation above where P is the amount of money the farmers paid in millions of dollars and T is the year so this is how much they paid in millions of dollars t is the year but they're saying assuming 1991 is T equals zero what does a 3.5 3 mean in the equation so let's look at this so at t when in 1991 when t is equal to 0 this whole term is going to be equal to zero and the farmers are going to pay p is going to be a hundred so they're gonna pay a hundred million dollars in 1991 to maintain their crop these are all the farmers in Massachusetts now as T increments each time T increases by 1 the amount that the farmers pay is going to increase by three point five three times one so one way to think about is this is the rate of increase from year to year as T goes up a year the amount the farmers pay is going to increase by three point five three million dollars so let's see which of these choices are consistent with what I just said the cost for maintaining crops was three point five three million dollars in 1991 no that's just not true in 1991 this term is zero and it was a hundred million dollars the cost for maintaining crops was three point five three million in 2008 no that's not going to be true either because it's a hundred million in 1991 and then each year it's going to increase by three point five three million the cost for maintaining crops increased a total of three point five three million between 1991 and 2008 no it's going to increase three point five three million per year not over the entire the entire time span the cost for maintaining crops increased by three point five million three point five three million each year between 1991 and 2008 that is exactly right every time T and we go forward a year T increases by one it's going to increase we're gonna have three point five three times that one higher T so we're gonna increase the whole P by three point five three they're kind of rind