The growth constant k for this problem is 1.408
There are about 46884 bacteria in the dish after 20 hours
Step-by-step explanation:
The growth function is [tex]y=a(b)^{x}[/tex] , where
The growth equation is [tex]y=a(b)^{x}[/tex]
∵ There are 50 bacteria in pertri-dish at a certain time
∴ The initial value of bacteria is a = 50
∵ The growth constant factor is k
∴ [tex]y=50(k)^{x}[/tex], where y is the number of bacteria after x hours
∵ Six hours later, there are 390 bacteria in the dish
∴ y = 390 and x = 6
- Substitute them in the equation above
∴ [tex]390=50(k)^{6}[/tex]
- Divide both sides by 50
∴ [tex]7.8=(k)^{6}[/tex]
- Insert log to both sides
∴ [tex]log(7.8)=log(k)^{6}[/tex]
∴ ㏒(7.8) = 6 ㏒(k)
- Divide both sides by 6
∴ 0.1486824 = ㏒(k)
- Change ㏒ to base 10
∴ [tex]10^{0.1486824}=k[/tex]
∴ k = 1.408
The growth constant k for this problem is 1.408
Substitute the value of k in the equation
∴ [tex]y=50(1.408)^{x}[/tex]
∵ x = 20
∴ [tex]y=50(1.408)^{20}[/tex]
∴ y = 46884
There are about 46884 bacteria in the dish after 20 hours
Learn more:
You can learn more about the equations in brainly.com/question/12363217
#LearnwithBrainly
