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saw5 [17]
3 years ago
15

A culture of 10 bacteria is started, and the number of bacteria will double every hour. In about how many hours will there be 3,

000,000 bacteria?
Can some show me how to do this step by step using logarithm?

I will mark BRAINLIEST for whoever gives the best and correct answer

thank you
Mathematics
1 answer:
777dan777 [17]3 years ago
7 0

Answer: it will take 18.2 years

Step-by-step explanation:

We would apply the formula,

y = ab^t

Where

a represents the initial amount of bacteria.

t represents the doubling.

From the information given

a = 10

t = 1 hour

Since after 1 hour, the amount of bacteria multiplies by 2, then

y = 2 × 10 = 20

Therefore

20 = 10 × b^1

Dividing through by 10, it becomes

2 = b

The equation becomes

y = 10(2)^t

For 3,000,000 bacteria, then

3000000 = 10(2)^t

3000000/10 = (2)^t

300000 = (2)^t

Taking log of both sides, it becomes

Log 300000 = tlog2

5.477 = 0.301t

t = 5.477/0.301

t = 18.2 years

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Answer:

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Since is a one side test the p value would be:  

p_v =P(t_{(39)}>2.18)=0.0177  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and then the population mes seems to be higher than 2.1 at 5% of significance

Step-by-step explanation:

Data given and notation  

\bar X=2.2 represent the sample mean

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n=40 sample size  

\mu_o =2.1 represent the value that we want to test

\alpha=0.05 represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

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We need to conduct a hypothesis in order to check if the mean is higher than 2,1, the system of hypothesis would be:  

Null hypothesis:\mu \leq 2.1  

Alternative hypothesis:\mu > 2.1  

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t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

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Since is a one side test the p value would be:  

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