Question 1066143
A tomato plant is purchased at a garden supply store. The initial height of the plant its 37.6 in. The height of the plant h (in inches) is approximated by h= 22(t+5)^1/3 , where t is the time in days after planting. 

a. Determine the height of the plant 23 days after planting. 

I know the answer to a. is: 67

b. After being planted, it would take approximately ____ days for the plant to reach 4 ft.

So the equation would be: 48=22(t+5)^1/3 correct? When I simplify it I get a fraction. When I divide that fraction, I get the wrong answer. Help???
<pre>{{{matrix(2,1, " ", h = 22(t + 5)^(1/3))}}}
<b><u>a.</b></u>
{{{matrix(2,1, " ", h = 22(23 + 5)^(1/3))}}} ------ Substituting 23 for t
{{{matrix(2,1, " ", h = 22(28)^(1/3))}}}
{{{highlight_green(matrix(1,10, h, or, height, "=", "66.80495738,", rounded, up, to, 67, feet))}}}</pre>
<pre>
<b><u>b.</b></u>
4 feet = 48 inches 
{{{matrix(2,1, " ", 48 = 22(t + 5)^(1/3))}}} ----------- Substituting 48 for h
{{{matrix(2,1, " ", 48/22 = (t + 5)^(1/3))}}} -------------- Dividing by 22
{{{matrix(2,1, " ", 24/11 = (t + 5)^(1/3))}}} -------------- Reducing left side
{{{matrix(2,1, " ", (24/11)^3 = (t + 5)^((1/3) * 3))}}} ------ Raising each side to the 3<sup>rd</sup> power 
{{{(24/11)^3 = t + 5}}}
To grow to 4' or 48", time taken, or {{{highlight_green(matrix(1,9, t, "=", (24/11)^3 - 5, "=", "5.386175808,", rounded, to, 5, days))}}}</pre>