We have that the rate of continuous buddy for starts at one thousand dollars per year and it will increase exponentially at a rate of five percent per year or four years. And what we want to do is find the present value and the accumulated interest earned a three point five percent, which is going to be compounded continues. So to find accumulated, we need to find present value. So let's first, we'LL have a fine present value, so recall the present value is equal to zero to tea or capital. T is going to be our time interval with the function F thirty, which tells us our rate of money, which will bring even her here multiplied by E to the negative. Our little teeth beauty, where this little are supposed to be our raped, our interests that we're getting. So we're told that the money flow so F t is described by this part here, so it starts at one thousand dollars and an exponentially increases at five percent per year. So this time is that F A T is going to be so. It starts at one thousand and then there's going to be more supplied by E since it's exponentially increasing times zero point zero bye t. So this here will describe our value because, well, we plug in one into this. It would be one thousand times E to the zero point zero, which would be just that much more times a thousand. And so we have that. So we go ahead and plug this in to our present value. Christians were zero R time. Interval is going to be or so That's our capital. T f t. Like you said over there was gonna be one thousand five times e to the negative. So are are Is this three point by person here? So this is our little r. So this would be zero point zero zero zero points re five t and what we're going to do now Oh, drop that teeth right there. So I'm gonna first factor out of one thousand. I still have my interval from zero or and then I'm going to combine these two exponential tze and that will give what hold on our money one serious before. So this will be a being the zero point zero one five t and she might recall to integrate this is going to be e zero point zero one five t divided by its new power zero point zero one five and then we want to evaluate this from zero to four. So it's one thousand provided. So that's not really nice. Number two right down. But it will be too. So two thousand time for one thousand a thousand times, two hundred this one one, two, three, two hundred thousand divided by every. And then we want to evaluate this expression here at four injured. So when I funded for into the zero point zero one, our teeth end up with times, for this would be he to the point zero six and then subtract all to the zero, which was just being one. And so now this belly here will be approximately. Tell him he point zero six, which is about one point oh six. Subtract off one So the inside will be about point zero six and then we multiply that by two hundred thousand divided by three. So we end up about four thousand one hundred two points for war. So four thousand one hundred twenty dollars and four cents. And this here will be our who wasn't value and you might recall to find our accumulated. So, you know, emulated This here is equal to e to the r capital tee times our present value so e to the r capital t so capital tears or R is going point five percent. So this will be he to the zero point zero six and then p is the value just pounds approximately four thousand won twenty two point four four. And this here is approximately two more purpose. The last you had by you need to be point six, which will be about four thousand three hundred and seventy seven dollars and thirty five six. And so then this here will be our accumulated about.