I need help figuring out how to solve this problem.The rate of photosynthesis R for a certain plant depends on the intensity of light x, in lumens, according to R(x) = 270x - 90x^2. a. sketch the graph of this function on a meaningful windowb. determine the intensity x that gives the max rate of photosynthesis.

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Hubert KochLv2

27 Oct 2019

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must understand functions to be able linearize. First let's review what graphs of certain functions looks like. Sketch the shape of each type of y vs. x function below. k is listed as a generic constant of proportionally. Linear y = kx Inverse y = k/x Inverse Square y = k/x^2 Power y = kx^2 You will notice that only the linear function is a straight line. We can easily find the slope of our line by measuring the rise and dividing it by the run of the graph or calculating it using two points. The value of the slope should equal the constant, k, from the equation. Finding k is a bit more challenging in the last three graphs because the slope isn't constant. This should make sense since your graphs aren't linear. So how do you calculate the constant, k? You need to transform the non-linear graph into a linear graph in order to calculate a constant slope. You can accomplish this by transforming one or both of the axes for the graph. The hardest part is figuring out which axes to change and how to change them. The easiest way to accomplish this task is to solve your equation for the constant. Note in the examples from the last page there is only one constant, but this process could be done for other equations with multiple constants. Instead of solving for a single constant, put all of the constants on one side of the equation. When you solve for the constant, the other side of the equation should be in fraction form. This fraction gives the rise and run of the linear graph. Whatever is in the numerator is the vertical axis and the denominator is the horizontal axis. If the equation is not in fraction form, you will need to inverse one or more of the variables to make a fraction. First let's solve each equation to figure out what we should graph. Then look below at the example and complete the last one, a sample AP question, on your own. State what should be graphed in order to produce a linear graph to solve for k. Inverse Graph Vertical Axis: _____ Horizontal Axis: _____ Inverse Square Graph Vertical Axis: _____ Horizontal Axis: _____ Power (Square) Graph Vertical Axis: _____ Horizontal Axis: _____

use synthetic division to find 1. x^3+4x^2-x-4=0; 1

2. 2x^4-17x^3+51x^2-63x+27=0; 3 ,1

3.the revenue from sale of a product is given by R= 250x-5x^2-x^3. if the sale of 5 units gives a total revenue of $1000, use synthetic division to find another number units that will give $1000 in revenue.

4. The model y=0.000447x^3-0.0361x^2+0.615x+7.966, where x =0 in 1960, gives America personal savings rate for selected years from 1960 to 2009. In what year after 1970 is the personal saving rate 9.4 according to the model ?

5.The number of college enrollment in thousand by recent high school graduate is given by f(x)= 0.2x^3-13.71x^2+265.06x+1612.56, where x is the number of years after 1960 when the number of enrollment was 2862 thousand.

a. set the functional equal to 2862 and rewrite the resulting equation with 0 on one side.

b. set the nonzero side of the equation in part equal to y and graph this function on the windows [25, 50] by [-50, 50]. use the graph to find integer solution to this equation.

c. use synthetic division to find a quadratic factor

d. use quadratic formula to find any other any other solution to this equation

e. use the information to determine the years in which the number of enrollment was 2862000

**the text is what is contained in the picture**

1. Consider first a linear equation: 3x â 1 = 5.

a. Use a graphing utility to show y₁= 2x â 1 and y₂=5 and determine the point of intersection. Make a sketch and label it.

b. How does the graph in part (a) relate to the solution set of the equation 3x â 1 = 5?

c. To solve the equation 3x â 1 =5 algebraically, the first step is to add 1 to both sides of the equation. Use a graphing utility to show y₁=3x and y₂=6, and determine the point of intersection. Make a sketch and label it. How does this graph relate to the equation 3x=6?

d. The final step to solve the equation is to divide both sides of the equation by 3. Use a graphing utility to show y₁=x and y₂=2, and determine the point of intersection. Make a sketch and label it. How does this graph relate to the equation x=2?

e. The algebraic steps to solve the equation 3x â 1 = 5 produce two equations: 3x=6 and x=2. How do the graphs you sketched above represent the fact that these equations are equivalent to the original?

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