Model Exponential Growth Question :A sample of bacteria is growing at a continuously compounding rate. The sample triples in 10
1 answer:
Answer:
The bacteria count after
days is represented by
where indicates the starting amount of bacteria.
Step-by-step explanation:
In the sample, the bacterial population triples every 10 days, which implies that at the completion of the first 10 days, the bacterial count reaches
where denotes the original count of bacteria in the sample.
Following the second set of 10 days, the bacterial count becomes
after the third set of days,
and this pattern continues.
This leads us to the formula for the bacterial population after the nth period of 10 days, expressed as
where signifies the nth 10-day segment.
Since equals 10 days, we arrive at
which simplifies to
By substituting this back into , we find:
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Answer:
Step-by-step explanation:
Given data and notation
indicates the sample mean
refers to the sample standard deviation
is the sample size
represents the value we are testing.
indicates the significance level for the hypothesis test.
t refers to the statistic of interest.
is the p-value for the test (the variable we are interested in).
Formulate the null and alternative hypotheses.
I will set up the hypotheses to verify if the mean weight falls below 4 ounces, formalizing:
Null hypothesis:
Alternative hypothesis:
Since our sample size is < 30 and the population standard deviation is unknown, it’s advisable to utilize a t test to compare the actual mean against the reference value, with the statistic calculated as follows:
(1)
t-test: "This test compares group means and is commonly utilized to determine if the mean is (greater than, less than, or not equal to) a specific value."
Calculate the statistic
We can substitute the provided information into formula (1):
To achieve a positive profit p(x)>0, we start with:
Next, we solve for x:
The parameters are:
a = -2
b = 7
c = -3
We will apply the quadratic formula:
This yields two results—one a fraction, the other a whole number. We focus on the whole number since the muffins sold must be a complete unit. Thus we conclude:
x>3
Next, we solve for x:
The parameters are:
a = -2
b = 7
c = -3
We will apply the quadratic formula:
This yields two results—one a fraction, the other a whole number. We focus on the whole number since the muffins sold must be a complete unit. Thus we conclude:
x>3