Question

Writing and evaluating a function modeling continuous. The area covered by a certain population of bacteria increases according to a continuous exponential growth model. Suppose that a sample culture has an initial and an observed doubling time of 7 days. area of 2.5 mm? . Din 몸 (a) Lett be the time (in days) passed, and let y be the area of the sample at time t. Write a formula relating y tot. Use exact expressions to fill in the missing parts of the formula. Do not use approximations Х $ ? -0.01 (b) What will the area of the sample be in 16 days? Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

y = A e bt Let, be the model a) when t=0 A l =) A = 2.5 2.5 = y = 2.5 so, at taz, y = 2*2.5 = 5 76 so 5 = 2.5 e => 76 = ln(2) [since, encem) =m] 7 en123 => b= en (2.t 7 so, y = 2.5e b) art t =16, en(2).16 -) 7 y = 2.5 e Ž 12.2 so, the are of the sample will be 12.2 mm after 16 days.