Math

QuestionJunior starts with 10 cents and adds 2 pennies daily. Find the equation, graph it, and create a table for this.

Studdy Solution

STEP 1

Assumptions1. Junior starts with10 cents in his piggy bank. . He adds cents to his piggy bank each day.
3. We are asked to create a table, draw a graph, and write an equation to model this situation.

STEP 2

First, let's create a table to represent the situation. The table will have two columns one for the number of days (starting from0) and one for the total amount of money in the piggy bank.
DaysTotal Amount (cents)01011221416n?\begin{array}{|c|c|} \hline\text{Days} & \text{Total Amount (cents)} \\ \hline0 &10 \\ 1 &12 \\ 2 &14 \\ &16 \\ \vdots & \vdots \\ n & ? \\ \hline\end{array}

STEP 3

Next, we need to find a pattern in the table to write an equation. We can see that for each day, the total amount increases by2 cents. This suggests that the relationship between the number of days and the total amount is linear.

STEP 4

We can write an equation to represent this linear relationship. Let's use dd to represent the number of days and AA to represent the total amount. Since Junior starts with10 cents and adds2 cents each day, the equation isA=2d+10A =2d +10

STEP 5

Now, let's complete the table using the equation. For any day nn, the total amount AA in the piggy bank is given by A=2n+10A =2n +10.
DaysTotal Amount (cents)010112214316n2n+10\begin{array}{|c|c|} \hline\text{Days} & \text{Total Amount (cents)} \\ \hline0 &10 \\ 1 &12 \\ 2 &14 \\ 3 &16 \\ \vdots & \vdots \\ n &2n +10 \\ \hline\end{array}

STEP 6

Finally, let's draw a graph to represent this situation. The x-axis represents the number of days and the y-axis represents the total amount in the piggy bank. The graph is a straight line that passes through the point (0,10) and has a slope of2, which means for every unit increase in the number of days, the total amount increases by2 cents.
Unfortunately, I can't draw a graph here, but you can easily do it using any graphing tool. Just plot the equation A=2d+10A =2d +10.
The equation for this situation is A=2d+10A =2d +10, where AA is the total amount in the piggy bank and dd is the number of days.

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