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2.5.89-BE Assigned MedlaThe total sales of a company (in millions of dollars) months from now are given by S() = 0.0113 +0.71? + 2t+7. (A) Find S'(t). (B) Find...

Question

2.5.89-BE Assigned MedlaThe total sales of a company (in millions of dollars) months from now are given by S() = 0.0113 +0.71? + 2t+7. (A) Find S'(t). (B) Find S(6) and S'(6) (to two decimal placos) (C) Interpret S(14) = 199.64 and 5'(14) = 27.48

2.5.89-BE Assigned Medla The total sales of a company (in millions of dollars) months from now are given by S() = 0.0113 +0.71? + 2t+7. (A) Find S'(t). (B) Find S(6) and S'(6) (to two decimal placos) (C) Interpret S(14) = 199.64 and 5'(14) = 27.48



Answers

A company's total sales (in millions of dollars) $t$ months from now are given by $$ S(t)=0.03 t^{3}+0.5 t^{2}+2 t+3 $$ (A) Find $S^{\prime}(t)$ (B) Find $S(5)$ and $S^{\prime}(5)$ (to two decimal places). Write a brief verbal interpretation of these results. (C) Find $S(10)$ and $S^{\prime}(10)$ (to two decimal places). Write a brief verbal interpretation of these results.

For the following problem we have that accompanies total sales and millions of dollars is given as S. F. T. Equals two times Square of the past 10. Um And we want to use the four step process to find s. Prime of T. So what this process is going to look like is when we calculate the derivative, we write this as Key to the 1/2 or the function to the 1/2. And then we see that we use the product or the power rule. So we end up getting that S. Prime of T. Is going to equal. We multiply the one half time to to that just becomes one. So we're left with T. Plus. Can Is a negative 1/2. Now we want to evaluate Sf 15. We see that S. F. 15 would be 25 in here so that's two times five is 10. But as prime of 15 would be a different value.

As of t equal to 0.15 Time to to the power for both 0.4 tq plus 3.4 the Squire plus 10 times t negative three. So here you can see that a company total sales in millions of dollars t months from now are Cuban by sfp. So here in part A we have to find the delivery of s of T. So here you can see that the delivery of s of T equal to did anybody see you point See you 15 time to to the powerful plus the derivative of 0.4. Due to the pole three, the day would evolve 3.4 the square plus the derivative of 10 d Look negative negative delivery of three. So here you can see that the derivative of a softie equal to now. Here we apply the power rule and we get 0.15 times four time de que close 0.4 times three time The Squire bless 3.4 times two d blues. You can see that we get 10 and we know that the delivery of constant is zero. So we put here zero negative zero. Now we simplify that and we get the derivative of S of T equal to zero point 06 de que close 1.2 the Squire plus 6.8 d plus 10. So it is our final answer for part A. Now it's all part B here we have to find as a full. So here we have to put equal to four and we get 0.15 Fall to the power full close 0.4 time. Fall to the power three blows 3.4 time fall to the power to plus 10 time for negative three. Now we simplify that and we get as a full equal to 120 point 84 So here you can see that 120 $0.84 millions. Now we have to find the delivery of as a fool equal to 0.6 four to the power three. Close one point two. Fall to the power two blows 6.8 time. Cool. Close to 10. No, we simplify that and we get derivative of s of four equal to 60 point 25 24 30 to 4 And here you can see that 60.24 dollars millions per month. So here you can see that after four months, the total cell is 120.84 million dollars and is increasing Ah, a red oh, 60.24 million dollars for a month. So it is a final answer for part B. Now it's all part C. So here we have to find as of eight. So here we know that we have to put equal to eight and we get 0.15 time eight to the power four plus zero point full. Add to the power three list 3.4 eight to the power to blues 10 times eight Negative three. Now we simply further and we get as of eight equal to 560 0.84 So here you can see that 500 60.84 million dollars Now. After that, we have to find the delivery of s of eight equal to 0.6 time eight to the power three plus 1.2 time eight to the power to plus 6.8 times eight plus 10. Now we simplify that and we get the derivative of S of eight equal to 100 71 point 92 So you can see that here. 171.92 million dollars for months. So here we can say, after eight months, the total cell and 500 60.84 million dollars and is increasing. Uh huh. A red off 171.92 million dollars per month. So it is a word.

For the income. We want to use the four step process to find the Derivative as we saw before. The derivative is going to be key plus 10 to the negative one half. And we know that as prime of T or S of 10, if we put a 10 in here is going to be a square root of 20 Times two. So to route 20 And then if we put a 10 in here, that's going to be one over the square root of 20. As our answer, um We can estimate the total sales after 11 months and 12 months, Which we see would be s of 11 s of 12. Well that would just be increasing this by the small amount of the slope that we have based on the initial amount. So if we start off with two route 20 and then we know the slope at this point is one over route 20 we can add that little bit and that will take us to S equals 11 for the slope.

A bite. Is it IgE list all one. It is January 2000 14 putting the value we get as sick. Listo 2.7 Bless going for one for two. Multiply by one less no point to Monday. Play by a sign ALS by multiply by one divided by six minus Bye bye. By solving this, we get as a quest to open seven less 0.1 for two. Bless you're going to sign ALS Bye bye. Three minus off by bitey Sign is in old function So that SZ Callisto who claim seven bless 0.1 for two minus 2.2 sino Bye bye t no. By putting the value we get s equals 2.7 Yes, 0.14 minus. You goingto multiply by three divided right toe. By solving this, we get asked us to going nine 37 Matiz equates to 94. Your nets now be by these eight equals two for being 70. Well 2000 15 putting the value we get as sick Must Duplin seven. Yes. 0.14 to my reply by for being less 2.2 My reply by Sino by multiply by four B divided by six minus bye bye do. By solving this, we get as it was to open seven less 1.9 Double eight. Yes. You point to sign ALS 11 by by six The angle realizing why didn't fort they sign is negative You the it Afrin But I have friends. Angles is who by minus 11 by divided by six with music was to minus off by by six asic listo do 0.7 less 1.9 double eight bless. You'll find minus two point to sign off by by six. By solving this, we get 2.7 less 1.9 double a minus 2.2 multiply by one divided by two. And by solving this, we get asked us to 3.5 Double eight, which means 3 59 your nets Now see? But it is a eight list five which means May 2000 14. By putting the value we get a sequester who burned seven Bless going 14 to multiply by five Yes, goingto multiply by. Sign off by multiply by If I Yeah, I did by six minus bye bye. By solving this, we get as a quest to you 0.7? Yes, Buoying 71 less. You're going toe Multiply way Sign by divided by three by putting the value get as close to 2.7 last 0.71 less so kind too. Multiply by two or three divided by two Now, by simplifying this, we get as e questo Fire you point Stephen, which means 5 31 your nets now deep parties it be easy, Bristol 18. It means then, in July June 2015 s E questo open seven Bless 0.1 for two. Multiply by 18 less going to my reply by sign off by my reply by 18 Divided by six minus Bye bye to by simply find this big. It s e questo open seven. Yes. Going do point double If I six plus you're going to my reply by sign off fire by divided by two by co terminals We know that sign off. Five I divided by two easy questo Sign ALS Bye bye now. Putting this value in the question we get s a questo open seven less opine double 56 Plus no point to my reply by sign off bye bye to by simplifying this. We get a cyclist to open seven less two point double 56 bless you going to multiply by one. By simplifying this, we get s equals to seven point 456 which approximately will do 7 46 You're next. Hens ASIC listo 94 units Gen ready 2014 S Nicolas Dupont 3 59 units during their mental te ready 2000 15 ASIC list too. 5 31 units during the mental May 2000 14 and as Nicolas do 7 46 units during the month off June 2050.


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