Question

A bacteria colony increases in size at a rate of 4.0565e1.3t bacteria per hour. If the initial population is 54 bacteria, find the population four hours later. (Round your answer to the nearest whole number.) bacteria

Answer 1

Answer:

Population of bacteria four hours later $A=616.5187$  or nearest whole number

$A=616$

Step-by-step explanation:

Given,

Let amount of bacteria four hours later is=A

Rate of increase of bacteria per hour  $=\frac{\partial x}{\partial t}=4.0565e^{1.3t}$

Initial population of bacteria is =54

Time 4 hours

Find the population of bacteria 4 hours later

Solution,

$\int_{54}^{A}dx=\int_{0}^{4}4.0565e^{1.3t}dt$

$\left [ x \right ]_{54}^{A}=4.0565/1.3\left [e^{1.3t} \right ]_{0}^{4}$

$A-54=4.0565/1.3\left ( e^{1.3\times 4} -1\right )$

$A-54=562.5187301$

$A=562.5187301+54$

$A=616.5187$

Population of bacteria 4 hours later is$A=616$