Final answer:
To estimate the change in concentration when t changes from 10 to 50 minutes, substitute t = 10 and t = 50 into the given concentration function C(t) and find the concentrations. The change in concentration is the difference between the two concentrations.
Step-by-step explanation:
To estimate the change in concentration when t changes from 10 to 50 minutes, we can first find the concentration C(10) at t = 10 minutes and then find the concentration C(50) at t = 50 minutes. Finally, we can subtract the two concentrations to get the change in concentration. To find C(10) and C(50), we substitute t = 10 and t = 50 respectively into the given concentration function C(t) = 5+ 4t/1+t³-e⁻⁰.⁰³ᵗ.
Substituting t = 10 into the concentration function, we get C(10) = 5+ 4(10)/1+10³-e⁻⁰.⁰³ᵗ = 5+40/1+10³-e⁻⁰.⁰³ᵗ = 5+40/1+1000-e⁻¹/₃⁰= 5+40/1001-e⁻¹/₃⁰ = 5.039
Similarly, substituting t = 50 into the concentration function, we get C(50) = 5+ 4(50)/1+50³-e⁻⁰.⁰³ᵗ = 5+200/1+50³-e⁻⁰.⁰³ᵗ = 5+200/1+50³-e⁻⁰.⁰³ᵗ = 5+200/1+250000-e⁻¹.⁵⁰ = 5.2
The change in concentration when t changes from 10 to 50 minutes is C(50) - C(10) = 5.2 - 5.039 = 0.161 mg/ml.