Question

A sunflower is planted in a garden and the height of the sunflower increases by 7% per day. 2.79 days after being planted the sunflower is 15.7 inches tall. What is the 1-day growth factor for the height of the sunflower

Answer 1

The 1-day growth factor is found using the exponential growth formula. Given the sunflower's height after 2.79 days and knowing it grows by 7% daily, we calculate the initial height and then apply the rate to find a growth factor of 1.07.

Step-by-step explanation:

The question is asking for the 1-day growth factor for the height of the sunflower given that it increases by 7% per day. To find the growth factor, we need to use the formula for exponential growth, which is:

Final height = Initial height x (1 + rate of growth) ^ time

We know the final height (15.7 inches) and the time (2.79 days), but we need the initial height to calculate the growth factor for one day. We can rearrange the formula to solve for the initial height first:

Initial height = Final height / (1 + rate of growth) ^ time

Once we find the initial height, we can insert the 7% growth rate as 0.07 and solve for the 1-day growth factor, which would be 1 + 0.07, or 1.07.

Answer 2

Step-by-step explanation:

Using the growth formula

H = H₀ ( 1 + r) ^n

where H is the present height, H₀ is the initial height at which the plant was grown, r is the rate and n is the number of days

H = H₀ ( 1+0.07)^2.79

15.7 = H₀ (1.07)^2.79

15.7 / (1.07)^2.79 = H₀

H₀ = 13 inches

Height after one day = 13 ( 1.07)¹ = 13.91 and the growth factor is 1.07