Find the ratio $\dfrac{606.42}{604.00}$ and then $\dfrac{608.84}{606.42}$. Are these ratios about the same? What number are you multiplying by each year?

An exponential growth formula for money with a constant percentage rate often looks like $n = a(1+r)^t$, where $a$ is the starting amount and $r$ is the decimal interest rate. Identify $a$ and $r$ from the table, then see which option fits that pattern.

In Desmos, create a table with $x$ for time and $y$ for amount. Enter the points $(0,604)$, $(1,606.42)$, and $(2,608.84)$ so you can see the data on the graph.

For each option, type an equation using $x$ instead of $t$, such as $y = (1+0.004)^x$, $y = 604^x$, $y = 604(1+0.004)^x$, and $y = 0.004^x$. Turn them on one at a time so you can see each curve clearly.

See which curve passes exactly through all three table points you entered. The equation whose graph goes through $(0,604)$, $(1,606.42)$, and $(2,608.84)$ is the model that matches the situation.

For an exponential growth situation like money in a savings account with a constant percentage rate, the amount after $t$ years is usually modeled by

where:

• $a$ is the initial amount (at $t=0$), and
• $b$ is the growth factor (the number you multiply by each year).

Use the row where $t=0$.

From the table:

• When $t=0$, $n = 604.00$.

So the initial amount is $a = 604$. Any correct equation must give $n=604$ when $t=0$, which means it must start with a factor of $604$. That tells you the model should look like

for some growth factor $b$. We will find $b$ next.

To find $b$, look at how the amount changes from one year to the next by taking a ratio.

From year 0 to year 1:

From year 1 to year 2:

The ratio is the same each year, so the growth factor is $b = 1.004 = 1 + 0.004$. This means the account grows by $0.4\%$ per year.

Substitute $a=604$ and $b=1+0.004$ into the exponential model:

This matches the data in the table and is the correct choice.