Question

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?

Answer 1

Answer:

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 $e^{\alpha t}$

The initial height is 9 ”, so the constant

         h₀ = 9”

Let's use the given values

       h = 15.1655”

       t = 5 days

       h / h₀ = $e^{\alpha t}$

      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 = $e^{0.104 5}$

        h / h₀ = 1,682

b) for t = 1 day

       h / h₀ = $e^{0.104 1}$

       h / h₀ = 1.11

c) for t = 7 days

       h / h₀ = e^{0.104 7}

       h / h₀ = 2.07