Math for Bus. & Soc. Sci. I- MATH-1324-342 Homework: Chapter 10 Applications Hom
ID: 3019184 • Letter: M
Question
Math for Bus. & Soc. Sci. I- MATH-1324-342 Homework: Chapter 10 Applications Homework Score: 0 of 1 pt 3 of 10 (3 complete) Life Sci 10.6.27 A culture contains 30,000 bacteria, with the population increasing exponentially. The culture contains 35 ,000 bacteria after 8 hours. a. Write a function in the form y yo e giving the number of bacteria after t hours. b. Write the function from part a in the form y yoa c. How long will it be until there are 55,000 bacteria? a. The exponential equation is (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check AnswerExplanation / Answer
a.y=y0ekt
35000=30000e8k
7/6= e8k
k=(1/8) ln(7/6)=0.019
y= 30000 e0.019t
b. y=y0at
35000=30000a8
a8=7/6
a=(7/6)1/8 =1.019
y=30000 (1.019)t
c.55000=30000(1.019)t
11/6= 1.019t
log(11/6)= t log 1.019
t=32.204hours