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
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.
