Let Y(t) be a population of yeast in a sugar solution that begins with a concentration of 70 yeast/ml. a. If the concentration of yeast is given by Y(t) = 70e", then differentiate this function to find the rate of increase in the concentration of yeast per hour. (Your answer should contain both t and r. ) Y' (t) = r70e^(rt) yeast/ml/hr. b. Find the value of r assuming that the concentration doubles every 3.2 hours. r = c. Evaluate the concentration of yeast at t = 1 hours and the rate of increase in the concentration of yeast per hour. Y(1) = yeast/ml. Y'(1) = yeast/ml/hr. Evaluate the concentration of yeast at t = 9 hours and the rate of increase in the concentration of yeast per hour. Y(9) = yeast/ml. Y'(9) = yeast/ml/hr.
Let Y(t) be a population of yeast in a sugar solution that begins with a concentration of 70 yeast/ml. a. If the concentration of yeast is given by Y(t) = 70e", then differentiate this function to find the rate of increase in the concentration of yeast per hour. (Your answer should contain both t and r. ) Y' (t) = r70e^(rt) yeast/ml/hr. b. Find the value of r assuming that the concentration doubles every 3.2 hours. r = c. Evaluate the concentration of yeast at t = 1 hours and the rate of increase in the concentration of yeast per hour. Y(1) = yeast/ml. Y'(1) = yeast/ml/hr. Evaluate the concentration of yeast at t = 9 hours and the rate of increase in the concentration of yeast per hour. Y(9) = yeast/ml. Y'(9) = yeast/ml/hr.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Let Y(t) be a population of yeast in a sugar solution that begins with a
concentration of 70 yeast/ml.
a. If the concentration of yeast is given by
Y(t) = 70e't,
then differentiate this function to find the rate of increase in the concentration of yeast per
hour. (Your answer should contain both ʼn and r. )
Y' (t) = r70e^(rt)
b. Find the value of r assuming that the concentration doubles every 3.2 hours.
r =
yeast/ml/hr.
c. Evaluate the concentration of yeast at t = 1 hours and the rate of increase in the
concentration of yeast per hour.
Y(1) =
yeast/ml.
Y'(1) =
yeast/ml/hr.
Evaluate the concentration of yeast at t = 9 hours and the rate of increase in the
concentration of yeast per hour.
Y(9) =
yeast/ml.
Y'(9) =
yeast/ml/hr.
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