Question

algebra: concepts and connections - plc
exponential growth functions
relating components of functions to their graphs
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 constant additive rate, rather than a multiplicative rate.
the graph will show an initial value that is lower on the ( y )-axis.

Explanation:

In the exponential function form $f(x)=a(b)^x$, the $a$-value is the initial value (the y-intercept when $x=0$). Decreasing $a$ (while keeping it positive) reduces this starting y-value, shifting the graph's starting point lower on the y-axis. The other option describes a general trait of exponential functions, not the effect of changing $a$.

Answer:

The graph will show an initial value that is lower on the y-axis.