Write the exponential model given two point 1) \( (9,140) \) and \( (10,250) \)

To build the exponential model based on your points, we can express it in the form \( y = a \cdot b^x \). Starting with the two points: 1. From \( (9, 140) \): \( 140 = a \cdot b^9 \) 2. From \( (10, 250) \): \( 250 = a \cdot b^{10} \) Now, dividing the second equation by the first gives us: \[ \frac{250}{140} = \frac{a \cdot b^{10}}{a \cdot b^{9}} \] This simplifies to: \[ \frac{25}{14} = b \rightarrow b \approx 1.7857 \] Now plug \( b \) back into one of the equations to find \( a \): \[ 140 = a \cdot (1.7857)^9 \] \[ a \approx \frac{140}{(1.7857)^9} \approx 22.56 \] Thus, the exponential model is: \[ y \approx 22.56 \cdot (1.7857)^x \] Now you have a vibrant model to predict values beyond your original data points!