leticia invests $200 at 5% interest. if y represents the amount of money after x time - periods, which…

Explanation:

Step1: Recall compound - interest formula

The formula for compound - interest in the form of an exponential function is $y = a(1 + r)^x$, where $a$ is the initial amount, $r$ is the interest rate per time period, and $x$ is the number of time periods.

Step2: Identify the initial amount

Leticia invests $a=$200$, so the initial value of the function (when $x = 0$) is $y(0)=200(1 + r)^0=200$.

Step3: Identify the growth factor

The interest rate $r = 5%=0.05$. The growth factor of the exponential function is $1 + r=1 + 0.05 = 1.05$. This means that for each unit increase in $x$ (time period), the value of $y$ increases by a factor of $1.05$.

Answer:

The initial value of the graph is 200. The graph increases by a factor of 1.05 per 1 unit increase in time.