Suppose there are 50 bacteria in pertri dish at a certain time. Six hours later, there are 390 bacteria in the dish.What is the growth constant, k, for this problem?How much bacteria are in the dish after 20 hours?
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Answer:
The growth constant k for this problem is 1.408There are about 46884 bacteria in the dish after 20 hoursStep-by-step explanation:The growth function is [tex]y=a(b)^{x}[/tex] , wherea is the initial valueb is the growth constant factorThe 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 = 1.408The growth constant k for this problem is 1.408Substitute the value of k in the equation∴ [tex]y=50(1.408)^{x}[/tex]∵ x = 20∴ [tex]y=50(1.408)^{20}[/tex]∴ y = 46884There are about 46884 bacteria in the dish after 20 hoursLearn more:You can learn more about the equations in brainly.com/question/12363217#LearnwithBrainly
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