thank you in advance! 7 3,5 028 Suppose that in a certain biology lab experiment

Question

thank you in advance!

7 3,5 028 Suppose that in a certain biology lab experiment, the number of bacteria is related to the temperature T of the environment by the function N(T)-2T+250T 5000 (40 sTs 90). Here, NCT) represents the number of bacteria present when the temperature is T °F. Also, T(t)-10t 50 (osts5). (a) Compute NITCe)] (b) How many bacteria are present when t-0 hr, when t = 2 hr? when t-5 hr? bacteria bacteria bacteria t=2hr t-5 hr Consider the following x 5)x + 2yx - 1) a) Find the domain, x and y-intercepts, vertical asymptote, and horizontal asymptote for the rational Domain

Explanation / Answer

N(T) = - 2T^2 + 250T - 5000

T(t) = 10t + 50

N[T(t)] = - 2 ( 10t + 50)^2 + 250 (10t+50 ) - 5000

= -2 ( 100t^2 + 1000t + 2500 ) + 2500t + 12500 - 5000

= -200t^2 - 2000t - 5000 + 2500 t + 12500 - 5000

combining like terms

= - 200t^2 + 500t + 2500

a) bacteria present at t = 0 hr

= -200(0)^2 + 500 (0) + 2500

= 2500 bacteria

b) t = 2

=  -200(2)^2 + 500 (2) + 2500

= 2700 bacteria

c) t = 5

- 200(5)^2 + 500(5) + 2500

= 0

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