Question

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. What is the 5-day growth factor for the height of the sunflower

Answer 1

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.

$y=a\cdot (1+r)^x$, where,

y = Final value,

a = Initial value,

r = Growth rate in decimal form,

x = Time.

Upon substituting initial value $a=8$, $x=5$ and $y=13.4805$, we will get:

$13.4805=8\cdot(1+r)^5$

$8\cdot(1+r)^5=13.4805$

$\frac{8\cdot(1+r)^5}{8}=\frac{13.4805}{8}$

$(1+r)^5=\frac{13.4805}{8}$

Now, we will take 5th root of both sides of equation as:

$\sqrt[5]{(1+r)^5} =\sqrt[5]{\frac{13.4805}{8}}$

$1+r =\sqrt[5]{1.6850625}$

$1+r =1.1100005724234515$

$1-1+r =1.1100005724234515-1$

$r=0.1100005724234515$

$r\approx 0.11$

Therefore, the growth factor is approximately 0.11 or 11%.