Measures how quickly the position of the object changes when time advances.
The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value
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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Kate: Please, for clarity, use " ^ " to denote exponentiation: 2x^2 + x − 4 = 0
And please include the instructions.
2x^2 + x − 4 = 0 can be re-written: 2(x^2 + (1/2)x - 2) = 0
Dividing both sides by 2 results in x^2 + (1/2)x - 2 = 0
Let's "complete the square:" x^2 + (1/2)x + (1/4)^2 - (1/4)^2 = 0
Then (x+(1/4))^2 = (1/4)^2
Taking the sqrt of both sides: x+1/4 = plus or minus 1/4
Solving for x: x = -1/4 plus or minus 1/4
Solving for x (continued): x = 0 and x = -1/2
Answer: 0.25
Step-by-step explanation:
the mean is 7.25. the median is 7. so, the difference is 0.25.
