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A plant has an initial height of 6 inches and grows at a constant rate of 3 inches each month. A second plant that also grows at a constant rate has an initial height of 2 inch and is 50 inches tall after 1 year. After how many months are the plants the same height?

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opudodennis

Answer:

4 months

Step-by-step explanation:

-Let the number of months it takes for their heights to equal be x and let h(x) be the height after x months.

#For plant 1, we equate height after x months as:

[tex]h(x)=6+3x[/tex]

#For plant 2, we equate height after x months and at a constant rate m:

[tex]h(x)=2+mx[/tex]

#we equate and solve for rate of growth, m in plant 2 as below:

[tex]h(x)=2+mx\\\\but\ h(12)=50\\\\\therefore r=\frac{50-2}{12}\\\\r=4 \ inches/month[/tex]

#We then equate the two heights after x months to solve for x:

[tex]h(x)_1=h(x)_2\\\\6+3x=2+4x\\\\6-2=4x-3x\\\\x=4[/tex]

Hence, the plants have the same height after 4 months

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