Welcome back, we’re ready to do part D and let me copy and paste that in as well. You see I don’t think that’s going to need to scraps so let me just remove that with the color other than yellow. There you go and let me copy and paste it. I'm just copying and pasted and I don’t know if you can read it but it’s helpful for me to view the problem on our clipboard.
The rate at which tickets were sold for—you know for over this range is modeled by r(t) let me write that in case you can't see it. This is the rate at which ticket were sold r(t) = 550 te(-t/2) tickets per hour base on the model how many tickets were sold by 3:00 PM? So our t = 3 to the nearest whole number, so that sometimes important you don’t want to give a decimal answer.
So this is the rate at which tickets are sold, right? So this is the derivative of the total tickets sold function, right? Or another way that we could drive it is the total ticket sold so let's called that, I don’t know, T sub—well, let me I don’t want to do t of t that’s lose up here. So let say the ticket sold as a function of time is going to be equal to the definite integral—well we could say at any time t the ticket sold and this the fundamental terms calculus I think it might be one of its colors or actually sometimes it is a fundamental term calculus. I was forgot my definitions.
But between time equal zero and t or if we want another ticket sold between time equal zero and t is equal to the integral of the rate at which the ticket sold was changing so that’s equal to 550 t e(-t/2) dt, all right, that’s it. And so if we want to know how many tickets were sold at time equal 3 that’s just equal to the definite integral from zero to 3 or we could also view it as the area under this curve from time equal zero to time equal 3 of 550 t e(-t/2) dt.
Now this going to go right here you can't solve an unethically using integration apart which is I just be called or reverse product rule but you only have 45 minutes to do all three of this problems and they let you use your graphing calculator and your graphing calculator is excellent at use doing definite integrals and they just want the number, right? So let's use our graphic calculators to get that number.
So let see I don’t want to copy, I don’t want—so how do we do that? We just do second the division button but that’s calk definite—let me use the definite integral and like what was—let see let me where I track that. So its 550 calculus is use x 550 times x times second e(-x) divided by 2, I think that’s the whole function, right that’s the whole function and let see my independent variable is x I just swap t for x there and I'm taking the integral from zero to 3, click enter let the calculator do the work this would have taken you quite a while if you actually do the integral yourself 972.78 and they want to us to round to the nearest whole number. So the nearest whole number is 973.
So we say 973 tickets sold by three 3:00 PM and we’re done that only took us four minutes and then we’re take you see and less if we didn’t have to explain it. Anyway, I will see you in problem number three.
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