i need help on this question i am stuck

Question

The concentration CC (in percent) of a drug in a patient's bloodstream tt hours after injection is given by C=35⋅(t/60+t^2)

a. What is the concentration of the drug after 2.5 hours? (round answer to two decimal places)

b. How long does this drug stay in someone's bloodstream? Assume that the drug is out of the patients system once the concentration has decreased to 0.6 %? (round to two decimal places)

 hours

c. What is the end behavior of the function?

1. as t→∞,C→35t→∞,C→35
2. as t→∞,C→3560t→∞,C→3560
3. as t→∞,C→∞t→∞,C→∞
4. as t→∞,C→−∞t→∞,C→-∞
5. as t→∞,C→0

Answer 1

For the first, substitute t=2.5, so C = (35 x 2.5) / (60 + 2.5^2) = 1.32075 .. = 1.32 % to 2 decimal places

For the second you need to find t, so that C(t) = 0.6

(35t) / (60 + t^2) = 0.6

35t = 0.6 (60 + t^2)

35t = 36 + 0.6t^2

0.6t^2 - 35t + 36 = 0

you can find t using the quadratic formula, or plot 0.6x^2 - 35x + 36 on Desmos and read off the x intercept

end behavior ( what happens as t gets very large positively to C(t)

you can plug in a large t, say t = 1000000 and find C(t) to get an estimate

or divide numerator and denominator of C(t) by t giving 35 / (60/t + t)

as t gets large numerator approaches infinity so C(t) approaches zero