## anonymous 5 years ago When t>1 the number of people coming daily to a tourist attraction gradually grows according to f(t)=(t)^0.5+5/(t)^0.5 hundreds after t days. What is the growth rate when t=9 days?

1. anonymous

just substitute 9 for t in your equation

2. anonymous

if you want the answer i canc alculate it its not too hard of a calculation., your problem takes form f(9) = 9 ^0.5 + 5/(9)^0.5 which becomes 3+5/3 which then if u simplify the fractions it becomes 14/3

3. anonymous

when you have problems like that, its basically asking for an exact value, because it is giving you an instantaneous moment, i.e. 9 days.

4. anonymous

for others viewing this, if i'm wrong plz let me know.

5. anonymous

does the function f tell you how many people are present at a given t or the rate at which they increase from day to day?

6. anonymous

this seems more like a simple calculus problem than algebra...

7. anonymous

I believe it tells how many people are present at a given t.

8. anonymous

time being replaced by 9 days no?

9. anonymous

JS, the answer is 7.41 people/day.

10. anonymous

then find $f^\prime(9)$

11. anonymous

why would you differentiate the equation to obtain growth?

12. anonymous

Perhaps I am differentiating the function incorrectly.. hmm

13. anonymous

i don't think it has to do with differentiation but that's my opinion.

14. anonymous

square root of 9=3 l mean 9^0.5=3 put 3 all instead of 9^0.5 result can be 14/3

15. anonymous

that's wat i thought as well.

16. anonymous

if the function tells you how many people are at the attraction at a given day then the rate at which the number of people is growing on a given day would be given by the derivative

17. anonymous

JS Why do you think diferentiation for this question

18. anonymous

if u differentiate the equation though, the proper differed equation is:$0.5t ^{-0.5} - 2.5 t ^{-1.5}$

19. anonymous

i didn't think it was differentiation., but in the case that i am wrong thats the differed equation. cuz when u substitute 9 in differed equation the value is wrong.

20. anonymous

Alright, thank you anyway!

21. anonymous

SLİM555 lm so sory l made a mistake your question asks rate that means tangent we have to take firt derivative of f(t) f'(t)=0.5t−0.5−2.5t−1.5

22. anonymous

exactly