The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$. Express that function as an equation if $A = \$ 28$ when $t = 1$ and $A = \$ 30$ when $t = 2$.
A) $A = 2 t - 26$
B) $A = - 2 t + 26$
C) $\quad A = 30 t + 26$
D) $A = 2 t + 26$
E) $A = 30 t - 26$

Question

Quizplus · Accepted Answer

We can use the slope-intercept form of a linear equation, which is
$$A = mt + b,$$
where $m$ is the slope and $b$ is the $y$-intercept. Since the function is linear, we know that the slope is constant. We can find the slope using the given information:
$$m = \frac{	ext{change in }A}{	ext{change in }t} = \frac{\$ 30 - \$ 28}{2 - 1} = \$ 2.$$
Now we can use the point-slope form of a linear equation to find $b$:
$$A - 28 = m(t - 1) \Rightarrow A - 28 = \$ 2(t - 1) \Rightarrow A = 2t - 26.$$
Therefore, the answer is $\boxed{	ext{(D)}}.$

The Amount AAA Of Money on Deposit For ttt Years in an Account Earning Simple Interest Is a Linear

The Amount $A$ Of Money on Deposit For $t$ Years in an Account Earning Simple Interest Is a Linear