Question

The following data represent the bacterial growth in a liquid culture over a number of days:

Day	0	4	8	12	16	20
Amount ×106	67.38	74.67	82.74	91.69	101.60	112.58

Determine the best equation to predict the amount of bacteria after 35 days using the parabolic model. (Round the final answer to two decimal places.)

The amount of bacteria after 35 days is  .

Answer 1

I Day Given, Day 4 8 121.15.204 Amount (10) 67.38| 74.67 82.74 9.69 1816 112.58 16 parabolic equation ya axborot & apply logarithmic on bothing X 4.2103 74.67 1.3863 ency=bo(a) + b +01 (3) It is in form y = AT BY Y=ln(y) I A=loca) x = locas y B=b. [x=day / y=Amount / x= ln ly=lny) 67.38 Inf 4.31311-21859742 82.74 2.0794 4.4457 9.182/ 2.9899 4-51846.1748 11.0278 101.6 2-7726 4.6210 7.672 12,8123 20 | 112.58 | 2.9957 4.7237 8.9794 14.150 Exclude the st date point. No. of date pointe nas (4 to 20) Sun Ex= 0)-719 EX Y = 53.3523 EY = 22-999 Ex? - 29.0823 12 91.69

Linear regression : EX EX kl.719 29.0823) (8) = (33:3533) solve the above equations in calculator A = 3.935760005 B=0.288579989 In(a) = 3.935761005 b = 0.248549789 a - exp(3.935761005) - 51.2011 0.24858 Amount y = 51. 2081 * x

Given, x = 39 days. - y = 51.2011 # 350.24858 y = 123.9092 Amount of bacterial at 35 days = 123.91 *10°

I hope this will help you.