Questions: Understanding Rational Inputs Review Warm Up Here are the graphs of two different exponential functions, f and g. 1. By what factor do the values of f grow when the input increases by 1? By 10? 2. By what factor do the values of g grow when the input increases by 1? By 10? Graph input by 1 input by 10 --------- 1 g

Solution Steps

The graph of \(f\) passes through the points \((0, 50)\) and \((1, 150)\). When the input increases by 1 (from 0 to 1), the output increases from 50 to 150. The factor by which \(f\) grows is \(150/50 = 3\).

To find how much \(f\) grows when the input increases by 10, we can use the fact that when the input increases by 1, \(f\) is multiplied by 3. Thus, when the input increases by 10, \(f\) will be multiplied by \(3^{10}\).

The graph of \(g\) passes through \((0, 100)\) and \((1, 250)\). When the input increases from 0 to 1, the output changes from 100 to 250. The growth factor is \(250/100 = 2.5\).

Similar to \(f\), since \(g\) grows by a factor of 2.5 when the input increases by 1, when the input increases by 10, the growth factor is \(2.5^{10}\).

Final Answer