The equation will be of the form:
![A(t)= A_{0} e^{rt}](https://tex.z-dn.net/?f=A%28t%29%3D%20A_%7B0%7D%20e%5E%7Brt%7D)
where A is the amount after t hours, and r is the decay constant.
To find the value of r, we plug the given values into the equation, giving:
![40=320e^{3r}](https://tex.z-dn.net/?f=40%3D320e%5E%7B3r%7D)
Rearranging and taking natural logs of both sides, we get:
![ln\ 0.125=3r](https://tex.z-dn.net/?f=ln%5C%200.125%3D3r)
![r=\frac{ln\ 0.125}{3}=-0.693](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bln%5C%200.125%7D%7B3%7D%3D-0.693)
The required model is:
Answer:
The hypothesis test is right-tailed
Step-by-step explanation:
To identify a one tailed test, the claim in the case study tests for the either of the two options of greater or less than the mean value in the null hypothesis.
While for a two tailed test, the claim always test for both options: greater and less than the mean value.
Thus given this: H0:X=10.2, Ha:X>10.2, there is only the option of > in the alternative claim thus it is a one tailed hypothesis test and right tailed.
A test with the greater than option is right tailed while that with the less than option is left tailed.
Answer:
false
Step-by-step explanation:
an integer is any number greater or less than 0
Answer:
They'll reach the same population in approximately 113.24 years.
Step-by-step explanation:
Since both population grows at an exponential rate, then their population over the years can be found as:
![\text{population}(t) = \text{population}(0)*(1 + \frac{r}{100})^t](https://tex.z-dn.net/?f=%5Ctext%7Bpopulation%7D%28t%29%20%3D%20%5Ctext%7Bpopulation%7D%280%29%2A%281%20%2B%20%5Cfrac%7Br%7D%7B100%7D%29%5Et)
For the city of Anvil:
![\text{population anvil}(t) = 21000*(1.04)^t](https://tex.z-dn.net/?f=%5Ctext%7Bpopulation%20anvil%7D%28t%29%20%3D%2021000%2A%281.04%29%5Et)
For the city of Brinker:
![\text{population brinker}(t) = 7000*(1.05)^t](https://tex.z-dn.net/?f=%5Ctext%7Bpopulation%20brinker%7D%28t%29%20%3D%207000%2A%281.05%29%5Et)
We need to find the value of "t" that satisfies:
![\text{population brinker}(t) = \text{population anvil}(t)\\21000*(1.04)^t = 7000*(1.05)^t\\ln[21000*(1.04)^t] = ln[7000*(1.05)^t]\\ln(21000) + t*ln(1.04) = ln(7000) + t*ln(1.05)\\9.952 + t*0.039 = 8.8536 + t*0.0487\\t*0.0487 - t*0.039 = 9.952 - 8.8536\\t*0.0097 = 1.0984\\t = \frac{1.0984}{0.0097}\\t = 113.24](https://tex.z-dn.net/?f=%5Ctext%7Bpopulation%20brinker%7D%28t%29%20%3D%20%5Ctext%7Bpopulation%20anvil%7D%28t%29%5C%5C21000%2A%281.04%29%5Et%20%3D%207000%2A%281.05%29%5Et%5C%5Cln%5B21000%2A%281.04%29%5Et%5D%20%3D%20ln%5B7000%2A%281.05%29%5Et%5D%5C%5Cln%2821000%29%20%2B%20t%2Aln%281.04%29%20%3D%20ln%287000%29%20%2B%20t%2Aln%281.05%29%5C%5C9.952%20%2B%20t%2A0.039%20%3D%208.8536%20%2B%20t%2A0.0487%5C%5Ct%2A0.0487%20-%20t%2A0.039%20%3D%209.952%20-%208.8536%5C%5Ct%2A0.0097%20%3D%201.0984%5C%5Ct%20%3D%20%5Cfrac%7B1.0984%7D%7B0.0097%7D%5C%5Ct%20%3D%20113.24)
They'll reach the same population in approximately 113.24 years.