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Approximately 14,000 bacteria are placed in a culture. Let P(t) be the number of bacteria present in the culture after t hours, and suppose that P(t) satisfies the differential eguation P'(t) = 0.55P(t) (a) Find the formula for P(t). P(t) = 14000e 55t (b) What is P(0)? (Give an exact answer.) P(0) = 14000 (c) How many bacteria are there after 6 hours? (Give your answer correct to the nearest integer.) 379577 bacteria (d) What is the growth constant? (Give an exact answer.) 55 (e) Use the differential equation to determine how fast the bacterla culture is growing when it reaches 140,000, (Give your answer correct to the nearest integer.) 77000 bacteria per hour (F) What is the size of the bacteria culture when it is growing at the rate of 55,000 bacteria per hour? (Glve your answer correct to the near est integer.) bacteria

Approximately 14,000 bacteria are placed in a culture. Let P(t) be the number of bacteria present in the culture after t hours, and suppose that P(t) satisfies the differential eguation P'(t) = 0.55P(t) (a) Find the formula for P(t). P(t) = 14000e 55t (b) What is P(0)? (Give an exact answer.) P(0) = 14000 (c) How many bacteria are there after 6 hours? (Give your answer correct to the nearest integer.) 379577 bacteria (d) What is the growth constant? (Give an exact answer.) 55 (e) Use the differential equation to determine how fast the bacterla culture is growing when it reaches 140,000, (Give your answer correct to the nearest integer.) 77000 bacteria per hour (F) What is the size of the bacteria culture when it is growing at the rate of 55,000 bacteria per hour? (Glve your answer correct to the near est integer.) bacteria

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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Just need help with part f. The rest are all correct.
Approximately 14,000 bacteria are placed in a culture. Let \( P(t) \) be the number of bacteria present in the culture after \( t \) hours, and suppose that \( P(t) \) satisfies the differential equation \( P'(t) = 0.55P(t) \). (a) Find the formula for \( P(t) \). \[ P(t) = 14000e^{0.55t} \] (b) What is \( P(0) \)? (Give an exact answer.) \[ P(0) = 14000 \] (c) How many bacteria are there after 6 hours? (Give your answer correct to the nearest integer.) \[ 379577 \text{ bacteria} \] (d) What is the growth constant? (Give an exact answer.) \[ 0.55 \] (e) Use the differential equation to determine how fast the bacteria culture is growing when it reaches 140,000. (Give your answer correct to the nearest integer.) \[ 77000 \text{ bacteria per hour} \] (f) What is the size of the bacteria culture when it is growing at the rate of 55,000 bacteria per hour? (Give your answer correct to the nearest integer.) \[ 100000 \text{ bacteria} \]
Transcribed Image Text:Approximately 14,000 bacteria are placed in a culture. Let \( P(t) \) be the number of bacteria present in the culture after \( t \) hours, and suppose that \( P(t) \) satisfies the differential equation \( P'(t) = 0.55P(t) \). (a) Find the formula for \( P(t) \). \[ P(t) = 14000e^{0.55t} \] (b) What is \( P(0) \)? (Give an exact answer.) \[ P(0) = 14000 \] (c) How many bacteria are there after 6 hours? (Give your answer correct to the nearest integer.) \[ 379577 \text{ bacteria} \] (d) What is the growth constant? (Give an exact answer.) \[ 0.55 \] (e) Use the differential equation to determine how fast the bacteria culture is growing when it reaches 140,000. (Give your answer correct to the nearest integer.) \[ 77000 \text{ bacteria per hour} \] (f) What is the size of the bacteria culture when it is growing at the rate of 55,000 bacteria per hour? (Give your answer correct to the nearest integer.) \[ 100000 \text{ bacteria} \]
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