composite function problem

T

typingken

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Can someone please help me do this problem?

The number of bacteria in a refrigerated food product is given by N(T) = 23 T^2 - 125 T + 39, for 6 < T < 36. The variable T is the temperature of the food.

When the food is removed from the refrigerator, the temperature is given by T(t) = 7 t + 1.5 , where t is the time in hours.

Find the composite function N(T(t)):

N(T(t)) = Is this (23T^2-125T+39) (7t+1.5) ???
I have no clue I am stumped on this one. Please help me out.

Find the time when the bacteria count reaches 9357

Time Needed =
 
A composite function, f(g(x)), is quite different from a product of functions, [f(x)][g(x)].

You have multiplied the two functions. You need, instead, to plug the one, T(t), into the other, N(T). That is, take the expression for T(t) = T, and plug this into N(T) wherever there is a "T". This will give you N(t).

Please let us know if you're needing lessons on this topic, and we can see about finding you some online instruction.

Thank you. :D

Eliz.
 
N(T(t)) =
N(7t+1.5) =
23*(t+1.5)²-125(t+1.5)+39 for t=1 to 3.5
Set that = 9357 and solve for t.
 
ok this is my work done as far as simplifying to find n(T(t))

23(t+1.5)(t+1.5)-125(t+1.5)+39
23(t^2+3.0t+3.0t+2.25)-250t-187.5+39
23t^2+69t+69t+51.75-250t-187.5+39
23t^2-112t-96.75


Can anyone spot my mistake on the math done above?
 
23(t+1.5)(t+1.5)-125(t+1.5)+39
23(t^2+3.0t+3.0t+2.25)-250t-187.5+39 duplicate & 125
23t^2+69t+51.75-125t-187.5+39
23t^2-56t-96.75
 
I still get the wrong anwser with 56t.
What are your thoughts on this? I am going to try and rework this out meanwhile
 
FOIL still works.
(t+1.5)² = t²+1.5t+1.5t+1.5²
I'm not infalible. I get t=3hrs 4.5min. What does the book say it should be?
-------------
Gene
 
I agree with your answer, Gene -- but this comes from N(T(t)) = 23(7t+1.5)^2 - 125(7t+1.5) + 39 = 9357.
 
Unfortunately I don't have a book for my online class but
time=3.075 was correct. I still haven't gotten to plugging in t for time though becuase
I am still trying to figure out were I went wrong on the "N(T(t)) =" part.

I am pretty confident the -96.75 part is correct.

I apologize I haven't picked up the concept by now but how did you get 3.075?
 
It should have been
23*(7t+1.5)²-125(7t+1.5)+39
I had a typo and dropped the 7. Then I cheated and graphed it with the correct value. Sorry.

Try it with that. :oops:
-------------------
Gene
 
How did you figure the time by graphing out of curiousity?
Ok so this is what I did for that problem

23(7t+1.5)^2-125(7t+1.5)+39
23(7t+1.5)(7t+1.5)-875t-187.5+39
23(14t^2+3.0t+3.0t+34.5)-875t-187.5+39
322t^2+69t+69t+79.35-875t-18.75+39
322t^2-737t+645 I still did the probllem wrong.


I must have worked that out wrong as well because I didn't get the correct anwser for
N(T(t)) =


I appreciate your helping!
 
I was lazy and used a TI graphing calculator.
You need to understand binomial multiplication.
(7t+1.5)^2 = as you said
(7t+1.5)(7t+1.5)
FOIL
First: multiply the two first terms
7t*7t
Outer: multiply the two outer terms
7t*1.5
Inner: multiply the two inner terms
1.5*7t
Last: multiply the two last terms
1.5*1.5
(7t*7t)+(7t*1.5)+(1.5*7t)+(1.5*1.5) =
49t²+21t+2.25
If it is squaring you can substitute 2O or 2I for OI but till you get in under your belt you should do it the long way.

You had
14t^2+3.0t+3.0t+34.5
You added the 7t's instead of multiplying.
You duplicated the 3.0t (from the first effort?) again. What could be duplicated is 1.5*7t = 10.5t. Duplicating that gives the 21t.
I don't know where the 34.5 came from.
One more time?
 
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