A bacterial culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria, and after 8 hours the count is 50,000. (a) Find the initial population. P(0) = 80 bacteria (b) Find an expression for the population after t hours. 80 (125()) P(t) = (c) Find the number of cells after 5 hours. (Round your answer to the nearest integer.) P(5) 894.427191 X bacteria (d) Find the rate of growth (in bacteria/hour) after 5 hours. (Round your answer to the nearest integer.) P'(5)=719.762516 X bacteria/hour (e) After how many hours will the population reach 200,000? (Round your answer to one decimal place.) t = 9.72270623 hours
A bacterial culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria, and after 8 hours the count is 50,000. (a) Find the initial population. P(0) = 80 bacteria (b) Find an expression for the population after t hours. 80 (125()) P(t) = (c) Find the number of cells after 5 hours. (Round your answer to the nearest integer.) P(5) 894.427191 X bacteria (d) Find the rate of growth (in bacteria/hour) after 5 hours. (Round your answer to the nearest integer.) P'(5)=719.762516 X bacteria/hour (e) After how many hours will the population reach 200,000? (Round your answer to one decimal place.) t = 9.72270623 hours
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 29E
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