Question

exponential growth functions
the graph represents the function $f(x) = 10(2)^x$.
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 graph will begin at a lower point on the y-axis.
the y-values will continue to increase as x-increases
the y-values will each be less than their corresponding x-values.
the graph will increase at a slower rate.

Explanation:

The original function is $f(x)=10(2)^x$, an exponential growth function where $b=2$. When $b$ is decreased but stays greater than 1, the base of the exponential term is smaller. A smaller base (still >1) means the function grows more slowly as $x$ increases. Additionally, exponential growth functions with $b>1$ always have $y$-values that increase as $x$-increases, regardless of the value of $b$ (as long as $b>1$). The starting $y$-intercept (when $x=0$) is $10$, which does not change, and $y$-values remain greater than their corresponding $x$-values for this function.

Answer:

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