Question

ponential growth functions
the graph represents the function $f(x)=10(3)^x$
how would the graph change if the $b$ value in the equation is decreased but remains greater than 1?
choose two correct answers
the graph will increase at a faster rate
the $y$-values will each be less than their corresponding $x$-values
the graph will begin at a lower point on the $y$-axis
the graph will increase at a slower rate
the $y$-values will continue to increase as $x$ increases

Explanation:

1. For an exponential growth function \(f(x)=a(b)^x\) where \(b>1\), decreasing \(b\) (still \(b>1\)) reduces the growth speed, so the graph increases slower.
2. Since \(b\) is still greater than 1, the function remains a growth function, so \(y\)-values keep rising as \(x\) increases.
3. The starting \(y\)-intercept is \(a=10\), which doesn't change with \(b\), so the starting point stays the same. A slower growth means \(y\)-values are lower than the original function's, not less than \(x\)-values. Faster growth is incorrect as \(b\) is decreased.

Answer:

• The graph will increase at a slower rate
• The y-values will continue to increase as x increases