The expression y = 4.998 · is the exponential function that passes through the points (- 1, 5 / 3) and (3, 135).
<h3>How to derive an exponential function that passes through two given points</h3>
Herein we find the location of two points set on Cartesian plane that belongs to an exponential function of the form:
Where:
- A - y-Intercept of the exponential function.
- B - Growth factor
- x - Independent variable.
- y - Dependent variable.
Which is equivalent to the following logarithmic expression:
㏑ y = ㏑ A + B · x
If we know that (x₁, y₁) = (- 1, 5 / 3) and (x₂, y₂) = (3, 135), then the following system of equations is generated:
㏑ (5 / 3) = ㏑ A - B
㏑ 135 = ln A + 3 · B
Then, we solve the system by numerical methods:
㏑ A = 1.609 (A = 4.998), B = 1.098
And the exponential function is equal to y = 4.998 · .
To learn more on exponential functions: brainly.com/question/11487261
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Answer:
Step-by-step explanation:
The confidence interval for population mean is given by :-
Given :
n=23, which is a small sample(n<30), so we use t-test.
Significance level:
Critical value :
Then , the confidence interval for population mean will be :-
Hence, the 95% confidence interval for the population mean is
Answer:
61.7% of container A is empty after the pumping is complete.
Step-by-step explanation:
The volume of a cylinder is calculated by the formula B×h, where B is the area of the base, or radius²×π.
The volume of cylinder A is 9²×π×10=810π.
The volume of cylinder B is 5²×π×20=500π.
The percent that will be used to fill container B is the complete volume of B out of A: ≈.61728395 which is 61.7% rounded to the nearest tenth.
Answer: Rob ate more crackers.
Symbol answer: 6/12 < 9/12
Step-by-Step explanation:
Common knowledge: Anytime you have the same numerator, with a different denominator, the one with the bigger denominator is always smaller. For example, if had a pizza with 6 slices and a pizza with 4 slices, the one with 6 slices and smaller and the one with 4 slices and bigger. Even though 6>4 that mindset has to change when thinking about a problem like this.
<em>Another explanation: </em>
<em>If you still don’t get it, simply find a common denominator, so we’ll choose 12. Take 3/6 and multiply that by 2/2 so you get 6/12 and then take 3/4 and multiply that by 3/3 on both the (numerator and denominator) and that equals 9/12.</em>
<em>So now you have the expression: 6/12<9/12.</em>
Answer:
49 = 7m
m = 7
Step-by-step explanation:
200 - 151 = 49
There are 49 M&M's left
m = M&M's per day
7(7) = 49