Math  /  Algebra

Question1\checkmark 1 2\checkmark 2 3 4 5 6 7 8 9 10 11
A plant is already 41 centimeters tall, and it will grow one centimeter every month. The plant's height, HH (in centimeters), after mm months is given by the following function. H(m)=41+mH(m)=41+m
What is the plant's height after 14 months? \square centimeters

Studdy Solution

STEP 1

What is this asking? How tall will a plant be after 14 months if it starts at 41 centimeters and grows 1 centimeter each month? Watch out! Don't forget the plant *starts* at a certain height, it doesn't start from zero!

STEP 2

1. Define the function
2. Substitute and solve

STEP 3

We're given a handy-dandy function that tells us the plant's height after a certain number of months.
It's right there in the problem: H(m)=41+mH(m) = 41 + m This tells us that the plant *starts* at a height of 41\textbf{41} centimeters, and for every month (mm) that passes, we *add* 1\textbf{1} centimeter to its height.

STEP 4

We want to know the plant's height after 14\textbf{14} months, so we'll **substitute** m=14m = 14 into our function.
Think of it like swapping out the mm for the number 14\textbf{14}: H(14)=41+14H(14) = 41 + 14

STEP 5

Now, we just need to do a little addition!
Adding 41+1441 + 14 gives us 55\textbf{55}.
So: H(14)=55H(14) = 55

STEP 6

After 14 months, the plant will be 55\textbf{55} centimeters tall!

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