Final answer:
To find an exponential model that fits the data points (6,160) and (7,210), we can use the general form of an exponential function. Plugging in the values of the data points, we can determine the values of a and b in the exponential model y = a*b^x.
Step-by-step explanation:
An exponential model is a mathematical model that represents exponential growth or decay. In this case, we have two data points: (6,160) and (7,210). To find an exponential model that fits these data points, we can use the general form of an exponential function, which is y = a*b^x, where a is the initial value, b is the growth factor, and x is the input variable.
Let's use the first data point (6,160) to find the value of a. Plugging in the values of x = 0 and y = 6,160 into the equation y = a*b^x, we get 6,160 = a*b^0. Since any number raised to the power of 0 is 1, we can simplify the equation to a = 6,160.
Now, let's use the second data point (7,210) to find the value of b. Plugging in the values of x = 1 and y = 7,210 into the equation y = a*b^x, we get 7,210 = 6,160*b^1. Dividing both sides of the equation by 6,160, we get b = 7,210/6,160. Simplifying this fraction, we find b ≈ 1.173.
Therefore, the exponential model that fits the data points (6,160) and (7,210) is y = 6,160 * 1.173^x.