Question

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Writing and evaluating a function modeling continuous... At the beginning of a study, a certain culture of bacteria has a population of 280. The population grows according to a continuous exponential growth model. Alter 21 days, there are 588 bacteria. X 5 (a) Lett be the time (in days) since the beginning of the study, and let y be the number of bacteria at time. Write a formula relating y tot Use exact expressions to in the missing parts of the formula Do not use approximations »1.0 (b) How many bacteria are there 23 days after the beginning of the study Do not round any intermediate computations, and round your answer to the nearest whole number

Answer 1

o KOJ => Let the population growth according to a continuous growth model is 3 y= A ekt * given at beginning of the study (t=o) population of the bacteria = 280 (4=280) from = 280 = Are A=280 *given After 21 days → population of bacteria = 588 h at t=21 y=588 from 588 = 2800 ek(21) eR (21) 588 - е. (21k = 2.1 280 take lm on both side ² ln (21 kj encanj Inne} → 21k Ine= ln (2:1) lne=1 → 21 K = k= ln (2-1) Een (2-1) 19.е. {l en (2.1) → 21 a Ansiver Put values of A &K en ① ² em: <2.1))+ y= = 280 After 23 days lat t=23) y= y = 28.2 in 4) - 23 = 631-05 4 631 Aftex 23 days = 631 Bacteria Answer