PreviousProblem ListNextpoint) Suppose that the value of yacht in dollars after t years of use is V(t) 375000e-0.14t Wnat i the average value of the yacht over its ...

Suppose that the value of a yacht in dollars after $t$ years of use is $V(t)=275,000 e^{-0.17 t} .$ What is the average value of the yacht over its first 10 years of use?

The given part in this question is, if a certain make off or don't nobody is perceived for $3 its trade value be off at the end. Off he yes is given by we'll eat equals two You don't 0.78 the multiplied by 0.85 the whole power B minus one. If the original cost T is equals to $25,000 equals two $25,000 then we have to find the value. After one year, four years and seven years we'll start with party in party. We have to find the value after veneers value off tees but well put equals to one. In this situation even equals toe You don't 0.78 multiplied by 25,000 multiplied by you don't 0.85 for the whole power you know, as they put equals to 11 minus one is zero who are simplifying it The value this 19,000 500 dollars. Now we will do part B. In this part we have to find the value After four years he will be or beautiful equals to 0.78 multiplied by 25,000 multiplied by 0.85 to the power or minus What data 0.78 multiplied by 25,000 multiplied by their appointed pipe. With the poverty, I'm simplifying it. You will get 195 double zero multiplied by 0.85 about what the value will be approaching it. 11,000 975 Moving on to party. In this part, we have to find the value. After seven years, he really beat Bella Feel seven equals to 0.78 multiplied by 25,000, multiplied by 0.85 to the power seven minus one. Do 2.7 years multiplied well. 25,000 multiplied by 0.85 with the power six. Well, simplifying it. The value will be approximately 7000. He ended. What? Thank you.

So now we have a charter boat and we know that at time zero That this value of the boat is $154,900 for that Charter boat. And that 16 years after purchase, they figure that the value of the But will be down to 46,100. And so we want to find in part a a linear model for this straight line depreciation, meaning it's going to drop the same amount each year. So let's are are function will end up looking like this slope times T plus V. And let's find our slope. Our slope is going to be the change in the value and we know it's negative because it's dropping. And So we have 46100 -154900. And that drop in value divided by 16, tells us that it is dropping negative is dropping $6800 per year. And our model will look like this. And then the y intercept we actually know is this value most of the time. We're not that lucky. We usually have to do some work to find it. But there's our model Now part B asked us to look at what that meaning of that slope is and we know the slope is -6800. And as I put down, if we include the units that this is in dollars and this is in dollars and this is in year and this is in year, we can find that our unit is in dollars per year. So we know that each year the value drops $68.00. Now, third thing we want to find is when will the value drop below $100,000? And we know it takes less than 16 years obviously. So let's yes our equation and find when it drops and we'll just do Well we can do this as when is this value? Less than 100,000. We can do it as an inequality or we can just find equal and know that time past that. But when is that? That value going to be less than 100,000. So we would subtract this 100 100,000 from this and that will give us -54900. And then we know we'll do a division and we know when we divide both sides by a negative number, That changes the sense of the sign. So now it becomes a greater than problem. And so let's find what 54,900 divided by 6800. I guess we could have chopped off a couple of those zeros and just under 5 49 divided by 68. That would have been smarter but didn't do that fast enough. So it takes 8.7 years. So basically um after approximately, after approximately eight years, the value Will be below 100,000.

Okay in discussion the market value of property is expected to engage according to the rules. V. T. equals to 80,000. He raised to the power is square root of T divided by two. Okay. Where we measured in the dollar and T. Is the time period in years from the present. And now one more thing is given if the rate of appreciation of the property is 9% and that is compound continuously for next eight years. So we can say here it is component continuously. So the city will be P. E. Raised to the power artie Okay, where are is given 9%. Okay. And T is ranges for next eight years. Okay. So we can say we will be P. E. Raised to the power zero R 0109 and T. Okay. And we are T ranges from 0-8. Okay. So this is the given rule that is a statement one and it is a statement to okay so we the we will equate these two Equation equal. Okay. And it will be a 2000. He raised to the power. The square root of T divided by two. Is the cost to P. Okay? He raised to the power 0.0 90. Okay. And it is VT Okay. So we will take care function be. That is often so it will be that is present value function. Okay? So from here Petey can be written as 80,000. He raised to the power. The square root of two divided by two. Divided by a raise to the power. 0.9 Okay. And now the present value function. It will be pretty close to $80,000. Also 80,000 areas to the power root tea by two. And this will go in the numerator and the exponent will become negative. He raised to the power minus 0.0 90. Okay. and now Beauty will be 80,000. And here s to the Power aid or the rest of the power be it will be raised to the power A minus B. So it will be raised to the power route divided by two minus 010 90. Okay that so this is the present value. Okay this is the expression for the present value for the property's market price. Okay. And this is valued for next four years. So we can say T. Is here from 0 to 8. Okay. So this will be the answer of party of discussion. And now part we Okay what is Beauty Expected to be in four years? So we will put You have to find out before that is 80,000. He raised to the power the square root of four x 2. Okay That is four x 2. That is zero minus -0.09 and T is four. Okay. So when we saw it using calculator, it will be approximate $151718. Okay. And this film with the final answer of part B of discussion. Thank you.

Okay, so we have to find the projected cost of a one year staying into joining. Tony noticed that we started from 2007. So 2020 minus two goes in. Seven is 13 tactical tour in value. We have 75 are actually the same equation, but and is now 13. It's a physical, too. What? Seeing four units into my calculator, I get 1417 h 1.96