Question

Solve the probkem. Must show all work for credit. Do not skip any steps. The function A = Age -0.00693% models the amount in pounds of a particular material after it's stored. The variable x represents the number of years since the material was stored. If 600 pounds of the material are stored now, how much time will need to pass for only 198 pounds of this material to remain? TTTT Paragraph 5. E T. Arial 3 (12pt)

Answer 1

A = A₀^-0.00693x

Here, A₀ = 600 lbs and A = 198 lbs

198 = 600*e^(-0.00693*x)

198 / 600 = e^-0.00693*x

33 / 100 =  e^-0.00693*x

Taking natural log both the sides

ln (33/100) = ln ( e^-0.00693*x)

ln (33/100) = -0.00693*x ln e

ln (33/100) = -0.00693*x

ln e = 1

x = -0.00693 / ln (33/100)

x = 160 years Answer