Which equation is represented by the graph below?
a. y= in x-3
b. y= in x-4
c. y=e^x -3
d. y= e^x -4

The answer is:

The equation that is represented by the shown graph is the equation from the option D.

Since we are given two types of functions, exponential and logarithmic, we need to remember that there is just an option that matches with the graph.

So, from the graph we can see that we are looking for an exponential function which intercepts are located at the point (0,-3) and a point which y-coordinate is equal to 0 and its x-coordinate is located at the x-axis between the number 1 and 2.

From the given options we can see that the only exponential function that intercepts the function at y equal to -3 is the fourth option, so, let's prove that:

Option D,

Finding the y-intercept, we need to make "x" equal to 0, so:

So, we know that the y-intercept point is located at (0,-3)

Finding the x-intercept, we need to make "y" equal to 0, so:

So, we know that the x-intercept point is located at (1.386,0)

Hence, we have that the axis interception points are (0,-3) and (1.386,0), so, the function that matches with the shown graph is the function from the option D.

Have a nice day!

Note: I have attached a picture for better understanding.

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.

the above table 1 will calculate the population size (n) after a certain length of time (t). all you need to do is plug in the initial population number (no), the growth rate (r) and the length of time (t). the constant (e) is already entered into the equation. it stands for the base of the natural logarithms (approximately 2.71828). growth rate (r) and time (t) must be expressed in the same unit of time, such as years, days, hours or minutes. for humans, population growth rate is based on one year. if a population of people grew from 1000 to 1040 in one year, then the percent increase or annual growth rate is 40/1000 x 100 = 4 percent.

step-by-step explanation: