identify the transformations that map rectangle A to rectangle A'. A) reflect over y-axis, reflect over line y = 5, then 3 units
1 answer:
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Answer:
Step-by-step explanation:
So, the function, P(t), represents the number of cells after t hours.
This means that the derivative, P'(t), represents the instantaneous rate of change (in cells per hour) at a certain point t.
C)
So, we are given that the quadratic curve of the trend is the function:
To find the <em>instanteous</em> rate of growth at t=5 hours, we must first differentiate the function. So, differentiate with respect to t:
Expand:
Move the constant to the front using the constant multiple rule. The derivative of a constant is 0. So:
Differentiate. Use the power rule:
Simplify:
So, to find the instantaneous rate of growth at t=5, substitute 5 into our differentiated function:
Multiply:
Subtract:
This tells us that at <em>exactly</em> t=5, the rate of growth is 51.72 cells per hour.
And we're done!
After the value of y is 4 does the exponential function definitely surpasses the linear function.
What is exponential function?
A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
Given
Use the graphing calculator to graph these functions: y1= 2x ; y2= 2x2 ; y3 = 2x.
As we can see y1=2x is a linear function and y3=2^x is a exponential function.
The graphs of y1 and y3 meet at 2 points i.e. at (1,2) and (2,4)
When you graph the equations their point of intersection is (2,4).
Therefore, when y > 4, the exponential function surpasses the linear function.
To know more about linear function click the link given below.
