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Answer:
About 0.6548 grams will be remaining.
Step-by-step explanation:
We can write an exponential function to model the situation. The standard exponential function is:
The original sample contained 510 grams. So, a = 510.
Each half-life, the amount decreases by half. So, r = 1/2.
For t, since one half-life occurs every 38 days, we can substitute t/38 for t, where t is the time in days.
Therefore, our function is:
One year has 365 days.
Therefore, the amount remaining after one year will be:
About 0.6548 grams will be remaining.
Alternatively, we can use the standard exponential growth/decay function modeled by:
The starting sample is 510. So, C = 510.
After one half-life (38 days), the remaining amount will be 255. Therefore:
Solving for k:
Thus, our function is:
Then after one year or 365 days, the amount remaining will be about:
Answer:
The degrees of freedom are given by:
And the p value would be:
Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week
Step-by-step explanation:
Information given
represent the sample mean for the growth
represent the sample standard deviation
sample size
represent the value that we want to compare
represent the significance level
t would represent the statistic
represent the p value
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is less than 2cm per week, the system of hypothesis are :
Null hypothesis:
Alternative hypothesis:
Since we don't know the population deviation the statistic is given by:
(1)
Replacing the info given we got:
The degrees of freedom are given by:
And the p value would be:
Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week