Updated on August 6, 2022

The number of bacteria in a culture is increasing according to the law of exponential growth. There are 145 bacteria in the culture after 2 hours and 415 bacteria after 4 hours. (a) Find the initial population. (Round your answer to the nearest whole number.) bacteria (b) Write an exponential growth model for the bacteria population. Let t represent the time in hours. y = (c) Use the model to determine the number of bacteria after 8 hours. (Round your answer to the nearest whole number.) bacteria (d) After how many hours will the bacteria count be 30,000? (Round your answer to two decimal places.) hr

## Answer

She си wth given by Find your – Yo ezk. culture is increasing number of bacteria in a Recording to the law of exponential grow- y = Yoekt Yo be the initias population. @ According to the question Duen t=2, y = 145 then from @) 145 – k → 70 = 145e-2x y : = 415 then from (1) wager 415= = 145 e [: You → 415 = 145e-2K 4K e-2x] » e 2k = 415 145 2K = m (445 * Ź ( • 415 0.52577 when t=4 4. e4k 个 À 5) from 22 [K 0-52577 ] 145 = Yoe 2×0.52517 § 145 a yo e-05154 145 x 2 | 05:54 & Yo * Yo = 51 [ Rouno to nearest whole number 280, One initos population is bactesia 51

51 e 0-52577 € 0.52577Xt 51 e – 6., Equation (1) becamese, [ y = 51 am k= 0.52577) y = So, the expoential growth model for the bacteria population is y Aus? When t=8 , then 0.5257748 ༡་ =sie ㅋ y ㅋ y ~ 3422 [ Round to nearest ohe One modle to determine the numbe of bacteria after 8 hourl î 6 3422 bacteria to hole number d) when 0.52577Xt y 1 = 30000 Then 30000 =5180 30000 * 5) 0000 50.52577xt = h 0:52577Xt – t = 069577- ( 30000) 3) to 12:13 [Round to two decimal places tonen So the bacteria count be 30000 [12.13 r.