Question

the graph of an exponential function passes through (1,−20) and (2,−80). find the exponential function that describes the graph.

Answer 1

To find the exponential function that describes the given graph, we can use the form y = ab^x. Using the given coordinates, we can solve a system of equations to find the values of a and b. Then, substitute these values back into the equation to obtain the exponential function.

Step-by-step explanation:

To find the exponential function that describes the given graph, we can use the form y = ab^x, where a is the initial value (the y-coordinate when x = 0) and b is the base of the exponential function.

1. Let's start by using the coordinates (1, -20) to find the value of a. Substituting x = 1 and y = -20 into the equation, we get -20 = ab^1.
2. Then, using the coordinates (2, -80), we can substitute x = 2 and y = -80 into the equation: -80 = ab^2.
3. Now we have a system of two equations: -20 = ab and -80 = ab^2. To solve this system, divide the second equation by the first equation to eliminate a: -80/(-20) = (ab^2)/(ab). This simplifies to 4 = b.
4. Substitute the value of b back into either of the original equations. Let's use -20 = ab: -20 = a(4^1). Solving for a, we find a = -5.

Therefore, the exponential function that describes the graph is y = -5(4^x).