Answer:
The growth factor is approximately 0.11 or 11%.
Step-by-step explanation:
We have been given that a 8-inch tall sunflower is planted in a garden and the height of the sunflower increases exponentially. 5 days after being planted the sunflower is 13.4805 inches tall.
We will use exponential growth formula to solve our given problem.
[tex]y=a\cdot (1+r)^x[/tex], where,
y = Final value,
a = Initial value,
r = Growth rate in decimal form,
x = Time.
Upon substituting initial value [tex]a=8[/tex], [tex]x=5[/tex] and [tex]y=13.4805[/tex], we will get:
[tex]13.4805=8\cdot(1+r)^5[/tex]
[tex]8\cdot(1+r)^5=13.4805[/tex]
[tex]\frac{8\cdot(1+r)^5}{8}=\frac{13.4805}{8}[/tex]
[tex](1+r)^5=\frac{13.4805}{8}[/tex]
Now, we will take 5th root of both sides of equation as:
[tex]\sqrt[5]{(1+r)^5} =\sqrt[5]{\frac{13.4805}{8}}[/tex]
[tex]1+r =\sqrt[5]{1.6850625}[/tex]
[tex]1+r =1.1100005724234515[/tex]
[tex]1-1+r =1.1100005724234515-1[/tex]
[tex]r=0.1100005724234515[/tex]
[tex]r\approx 0.11[/tex]
Therefore, the growth factor is approximately 0.11 or 11%.
