Hey there!
First, set up an exponential equation that represents the rate at which your original amount, 1000, gains interest:
y = 1000(1.24)^x
Y represents the value after X years. 1.24 represents the rate at which the money gains interest, 1 + 0.24 (your 24% interest rate in decimal form). 1000 is your original amount.
Now, set this equation equal to 64000, graph y = 64000 and y = 1000(1.24)^x on a graphing calculator, and see where the two equations intersect in order to solve for x.
They intersect when x is about 19.334, as seen in the graph below (it is very zoomed in so that you can see where the two functions intersect). Therefore, it will be about 19 years after the year in which you deposited the 1000 dollars before the money is worth 64000 dollars.
For this case we have the following equation:
![\sqrt [4] {2x-8} + \sqrt [4] {2x + 8} = 0](https://tex.z-dn.net/?f=%5Csqrt%20%5B4%5D%20%7B2x-8%7D%20%2B%20%5Csqrt%20%5B4%5D%20%7B2x%20%2B%208%7D%20%3D%200)
If we subtract both sides of the equation ![\sqrt [4] {2x + 8}](https://tex.z-dn.net/?f=%5Csqrt%20%5B4%5D%20%7B2x%20%2B%208%7D)
we have:
![\sqrt [4] {2x-8} = - \sqrt [4] {2x + 8}](https://tex.z-dn.net/?f=%5Csqrt%20%5B4%5D%20%7B2x-8%7D%20%3D%20-%20%5Csqrt%20%5B4%5D%20%7B2x%20%2B%208%7D)
To eliminate the radical we raise both sides of the equation to the fourth power:
![(\sqrt [4] {2x-8}) ^ 4 = (- \sqrt [4] {2x + 8}) ^ 4](https://tex.z-dn.net/?f=%28%5Csqrt%20%5B4%5D%20%7B2x-8%7D%29%20%5E%204%20%3D%20%28-%20%5Csqrt%20%5B4%5D%20%7B2x%20%2B%208%7D%29%20%5E%204)
Answer:
Option D
The best estimate is 17/60 .
Answers:
- a) The 40 students selected to participate in the survey (8*5 = 40).
- b) The population is the set of all students in his five classes combined.
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Explanation:
The teacher wants to know something about his students, so he's only focused on them and no one else. The teacher has 5 classes. Let's say each class has 40 students. That would mean 40*5 = 200 students total are taught by this bio teacher, and these 200 students make up the population. We're not considering any other student in this school since they are not in this teacher's class.
Once the population is well formed and well defined, the sample is drawn from the population. Specifically, the teacher is randomly selecting 8 people from each class. The teacher is using the stratified sample technique. Each class is a stratum, ie, a separate group. The plural of stratum is strata. Because there are 5 classes, and 8 people selected per class, this leads to an overall sample of 8*5 = 40 students. Those 40 students chosen randomly fairly represent the 200 students in the population. Therefore, this process is fairly unbiased.
Be sure not to mix stratified sampling with cluster sampling. Cluster sampling is not performed here because that would mean the teacher randomly selects say 2 classrooms (ie clusters) and samples <em>everyone </em>in each cluster selected. Instead, the teacher is only picking representatives from each class, as if those people were elected to office. As you can probably guess, cluster sampling can be expensive in terms of time and money, so if you need to apply a cluster sample, then it's best to make the clusters as small as possible but also make sure each cluster is reflective of the population.
