Homework Help is Here – Start Your Trial Now!
Math
Calculus
A bacteria 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. (3) P(t) = 80(125) (c) Find the number of cells after 7 hours. (Round your answer to the nearest integer.) P(7) = 22361 bacteria (d) Find the rate of growth after 7 hours. (Round your answer to the nearest integer.) P'(7) = bacteria/hour (e) When will the population reach 200,000? (Round your answer to one decimal place.) t = 9.7 hours

A bacteria 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. (3) P(t) = 80(125) (c) Find the number of cells after 7 hours. (Round your answer to the nearest integer.) P(7) = 22361 bacteria (d) Find the rate of growth after 7 hours. (Round your answer to the nearest integer.) P'(7) = bacteria/hour (e) When will the population reach 200,000? (Round your answer to one decimal place.) t = 9.7 hours

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 35E
See similar textbooks
icon
Related questions
Question

DO ALL OF THEM PLEASE

MAKE SURE THE ANSWERS ARE CLEAR TO TELL

A bacteria 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. ( ½) P(t) = 80 (125) (c) Find the number of cells after 7 hours. (Round your answer to the nearest integer.) P(7) = 22361 bacteria (d) Find the rate of growth after 7 hours. (Round your answer to the nearest integer.) P'(7) = bacteria/hour (e) When will the population reach 200,000? (Round your answer to one decimal place.) t = 9.7 hours
Transcribed Image Text:A bacteria 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. ( ½) P(t) = 80 (125) (c) Find the number of cells after 7 hours. (Round your answer to the nearest integer.) P(7) = 22361 bacteria (d) Find the rate of growth after 7 hours. (Round your answer to the nearest integer.) P'(7) = bacteria/hour (e) When will the population reach 200,000? (Round your answer to one decimal place.) t = 9.7 hours
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9780998625720
Author:
Lynn Marecek
Publisher:
OpenStax College
SEE MORE TEXTBOOKS