Question

farmer repfol started with some quects on his farm. after 7 days, he had 61 quects. after 15 days, he had 101 quects. assume a constant rate of change.
rate of change:
starting amount:

Explanation:

Step1: Define rate of change formula

Rate of change = $\frac{\text{Change in quects}}{\text{Change in days}}$

Step2: Calculate change in values

Change in quects = $101 - 61 = 40$
Change in days = $15 - 7 = 8$

Step3: Compute rate of change

$\text{Rate of change} = \frac{40}{8} = 5$

Step4: Set up linear equation

Let $y = mx + b$, where $y$=quects, $x$=days, $m$=rate.
$61 = 5(7) + b$

Step5: Solve for starting amount $b$

$61 = 35 + b$
$b = 61 - 35 = 26$

Answer:

Rate of change: 5 quects per day
Starting amount: 26 quects