Question

which linear equation is represented by the graph?$\boldsymbol{i = 140(0.09)t}$$\boldsymbol{i = 140(0.08)t}$$\boldsymbol{i = 140(0.07)t}$$\boldsymbol{i = 140(0.06)t}$

Explanation:

Step1: Recall linear form for balance

The account balance follows $B(t) = P + rt$, where $P=140$ (initial balance), $r$ is annual rate, and $B(t)$ is total balance at time $t$. Alternatively, the interest earned $I(t) = rt$, so total balance is $140 + I(t)$.

Step2: Calculate annual increase

Use point $(1, 149.8)$:
Increase in 1 year: $149.8 - 140 = 9.8$

Step3: Match to interest formula

Set $I(t)=140 \times r \times t$. For $t=1$, $I(1)=9.8$:
$9.8 = 140r$
$r = \frac{9.8}{140} = 0.07$
Thus, $I = 140(0.07)t$

Answer:

$I = 140(0.07)t$