A bean plant grows at a constant rate for a month. After 10 days, the plant is 30 centimeters tall. After 20 days, the plant is 50 centimeters tall. Which equation models the height of the plant, y, after x days?
To find the equation that models the height of the bean plant after x days, we can start by finding the rate at which the plant grows each day.
After 10 days, the plant is 30 centimeters tall.
After 20 days, the plant is 50 centimeters tall.
Therefore, the plant grows (50 - 30) = 20 centimeters in 20 - 10 = 10 days.
Therefore, the plant grows 20/10 = <<20/10=2>>2 centimeters per day.
Now, we can set up the equation.
Since the plant grows at a constant rate, we can use the equation y = mx + b,
where m is the rate at which the plant grows each day, x is the number of days, y is the height of the bean plant, and b is the initial height of the plant.
Since we are given that the plant is 30 centimeters tall after 10 days, we can plug these values into the equation:
30 = 2 * 10 + b.
Solving this equation, we find that b = 30 - 20 = 10.
Therefore, the equation that models the height of the plant after x days is:
y = 2x + 10.