A 9-inch tall sunflower is planted in a garden and the height of the sunflower increases exponentially. 5 days after being planted the sunflower is 15.1655 inches tall. a. What is the 5-day growth factor for the height of the sunflower? Preview b. What is the 1-day growth factor for the height of the sunflower? Preview c. What is the 7-day growth factor for the height of the sunflower?

a)  h / h₀ = 1,682

, b) h / h₀ = 1.11

, c)    h / h₀ = 2.07

Explanation:

For this exercise let's look for the growth equation, as they indicate that it is exponential

        h = h₀

The initial height is 9 ”, so the constant

         h₀ = 9”

Let's use the given values

       h = 15.1655”

       t = 5 days

       h / h₀ =

      α = 1 / t ln h / h₀

       α = 1/5 ln (15.1655 / 9)

      α = 0.104

       h = 9 e^{0.104 t}

a) the growth factor is the relationship between the initial value and the current value

        h / h₀ =

        h / h₀ = 1,682

b) for t = 1 day

       h / h₀ =

       h / h₀ = 1.11

c) for t = 7 days

       h / h₀ = e^{0.104 7}

       h / h₀ = 2.07

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)