Find the equation of the exponential function represented by the table below:xx yy00 1111 2222 4433 88
Question
Find the equation of the exponential function represented by the table below:xx yy00 1111 2222 4433 88
Solution 1
The given table represents an exponential function of the form y = ab^x.
The table is as follows:
| x | y |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
From the table, we can see that each time x increases by 1, y doubles. This means that the base of the exponential function (b) is 2.
When x = 0, y = 1. This is the initial value of the function, which is the coefficient a in the equation.
So, the equation of the exponential function represented by the table is y = 1*2^x, or simply y = 2^x.
Solution 2
The table represents an exponential function of the form y = ab^x.
Step 1: Identify the base (b) From the table, we can see that as x increases by 1, y doubles. Therefore, the base (b) is 2.
Step 2: Identify the initial value (a) The initial value is the y-value when x is 0. From the table, we can see that when x is 0, y is 1. Therefore, the initial value (a) is 1.
Step 3: Write the equation Now that we have identified a and b, we can write the equation of the exponential function. The equation is y = 1*2^x or simply y = 2^x.
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