Question

the graph represents the function $f(x) = 10(1.5)^x$
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 reach but 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:

The given function is an exponential growth function \(f(x)=10k^x\). When \(k>1\), it represents growth. If \(k\) is decreased but remains greater than 1, the growth rate slows (since the base of the exponential is smaller, the function rises less steeply). Also, exponential growth functions with \(k>1\) always have \(y\)-values that increase as \(x\) increases, regardless of the size of \(k\) (as long as \(k>1\)).

Answer:

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