Question 2 An exponential model y = a.6 passes through the points (0,9) and (3,243). What are the values of a and b?
1 answer:
Answer:
a = 9, b = 3
Step-by-step explanation:
The exponential function is
y = a
Find a and b by using the points it passes through
Using (0, 9 ) then
9 = a (
= 1 )
a = 9
y = 9
Using (3, 243 ) then
243 = 9b³ ( divide both sides by 9 )
27 = b³ ( take the cube root of both sides )
b = = 3
y = 9 ← exponential equation
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Answer:
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0141
The margin of error is:
M = T*s = 2.0141*170.5 = 343.4
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 390.47 - 343.40 = 47.07 units per month
The upper end of the interval is the sample mean added to M. So it is 390.47 + 343.40 = 733.87 units per month
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87