the graph represents the function f(x) = 10(2)^x. how would the graph change if the b value in the equation…

Explanation:

Step1: Analyze y - intercept

The y - intercept of an exponential function $y = a(b)^x$ is at $x = 0$, so $y=a(b)^0=a$. Changing the $b$ value ($b>1$) does not affect the y - intercept ($y = a$ when $x = 0$), so the graph won't begin at a lower point on the y - axis.

Step2: Analyze rate of increase

For an exponential function $y=a(b)^x$ with $a>0$ and $b > 1$, the larger the $b$ value, the faster the function grows. When $b$ is decreased (but $b>1$), the graph will increase at a slower rate.

Step3: Analyze general behavior

Since $b>1$, as $x$ increases, $y=a(b)^x$ (where $a = 10>0$) will have $y$ - values that continue to increase.

Step4: Analyze y and x relationship

For example, when $x = 2$ and $a = 10$, if $b = 2$, $y=10\times2^2=40$ which is greater than $x = 2$. In general, we can't say that $y$ - values will each be less than their corresponding $x$ - values for an exponential growth function $y=a(b)^x$ with $a>0$ and $b>1$.

Answer:

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