SOLUTION: 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

Algebra ->  Real-numbers -> SOLUTION: 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      Log On


   

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???
Answer by MathTherapy(10555) About Me  (Show Source):
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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???
matrix%282%2C1%2C+%22+%22%2C+h+=+22%28t+%2B+5%29%5E%281%2F3%29%29
a.
matrix%282%2C1%2C+%22+%22%2C+h+=+22%2823+%2B+5%29%5E%281%2F3%29%29 ------ Substituting 23 for t
matrix%282%2C1%2C+%22+%22%2C+h+=+22%2828%29%5E%281%2F3%29%29


b.
4 feet = 48 inches 
matrix%282%2C1%2C+%22+%22%2C+48+=+22%28t+%2B+5%29%5E%281%2F3%29%29 ----------- Substituting 48 for h
matrix%282%2C1%2C+%22+%22%2C+48%2F22+=+%28t+%2B+5%29%5E%281%2F3%29%29 -------------- Dividing by 22
matrix%282%2C1%2C+%22+%22%2C+24%2F11+=+%28t+%2B+5%29%5E%281%2F3%29%29 -------------- Reducing left side
matrix%282%2C1%2C+%22+%22%2C+%2824%2F11%29%5E3+=+%28t+%2B+5%29%5E%28%281%2F3%29+%2A+3%29%29 ------ Raising each side to the 3rd power 
%2824%2F11%29%5E3+=+t+%2B+5
To grow to 4' or 48", time taken, or