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Rational Expressions Applications Word Problem

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In a cancer research lab, you are observing the growth of cancer cells in two specimens, A & B. Specimen A presently has 2160 cells and specimen B has 1200 cells. After recording data for several days, you later determine that the number of cells in specimen A, N(A), is growing ny the formula:

N(A) = 24t^2 + 588t + 2160

where t is the number of days the specimen is in the test environment. Likewise, the data for specimen B indicates that its number of cells, N(B), is

N(B) = 36t^2 + 780t + 1200

a. Write a rational expression and simplify the ratio of N(A) to N(B). Show any intermediate steps.

b. On which day did the number of cancer cells in specimen B overtake that of specimen A?

c. How many cancer cells had developed in specimen B as of the day you calculated in (b)? Show your calculation and write this number using scientific notation.

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A rational expression wordproblem is solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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