Question

the given graph represents the function f(x) = 2(5)^x. how will the appearance of the graph change if the a value in the function is decreased, but remains greater than 0?
the graph will increase at a slower rate
the graph will show a decreasing, rather than increasing, function.
the graph will show an initial value that is lower on the y - axis
the graph will increase at a constant addition rate rather than a multiplicative rate.

Explanation:

The function is an exponential growth function of the form $f(x)=ab^x$, where $a=2$ and $b>1$ (here original $b$ is such that the graph grows quickly). When $b$ is decreased but remains greater than 1, the exponential growth rate slows down: the graph still increases, but not as rapidly as before. The other options are incorrect: the function stays increasing since $b>0$, the initial value (when $x=0$, $f(0)=2$) does not change, and it remains multiplicative growth, not additive.

Answer:

The graph will increase at a slower rate