Math for Bus Soc Sci I MATH1324342 Homework Chapter 10 Appl

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 Answer

Solution

a.y=y₀e^kt

35000=30000e^8k

7/6= e^8k

k=(1/8) ln(7/6)=0.019

y= 30000 e^0.019t

b. y=y₀a^t

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= 1.019^t

log(11/6)= t log 1.019

t=32.204hours