Final answer:
The height of the bean plant grows directly with the number of days passed. To predict its height after one week, we find the daily growth rate which is 0.64 cm/day. Multiplying this rate by 7 gives us a predicted height of 4.48 cm after one week.
Step-by-step explanation:
The question involves a direct variation problem in mathematics, where the height of a bean plant changes directly in proportion to the number of days since it sprouted. We are given that a bean plant is 1.92 cm tall after 3 days.
To find out how tall it will be in one week (which is 7 days), we need to establish the rate of growth per day and then use that rate to predict the height at 7 days.
To calculate the daily growth rate, we can use the formula for direct variation, y = kx, where y is the height of the plant, x is the number of days, and k is the constant of variation. Since we know the plant is 1.92 cm tall after 3 days, we find the constant k by dividing the height by the number of days:
k = 1.92 cm / 3 days
= 0.64 cm/day
Now, we can predict the height of the plant after 7 days by multiplying the daily growth rate (k) with 7 days:
Height after 7 days = 0.64 cm/day * 7 days
= 4.48 cm
Therefore, the bean plant will be approximately 4.48 cm tall in one week.