When t1 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?

Question

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?

anonymous · Answer

just substitute 9 for t in your equation

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

time being replaced by 9 days no?

anonymous · Answer

JS, the answer is 7.41 people/day.

anonymous · Answer

then find $$f^\prime(9)$$

anonymous · Answer

why would you differentiate the equation to obtain growth?

anonymous · Answer

Perhaps I am differentiating the function incorrectly.. hmm

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

that's wat i thought as well.

anonymous · Answer

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

anonymous · Answer

JS Why do you think diferentiation for this question

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

Alright, thank you anyway!

anonymous · Answer

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

anonymous · Answer

exactly