Students observing a caterpillar crawl on a tree noticed that the caterpillar crawled upwards 3/8 of an inch every minute. The caterpillar was already 4.5 feet off the ground when the students began observing.
Which function represents the total number of inches the caterpillar crawls after x minutes?
1. f(x)=3/8x+4.5
2. f(x)=3/8x+54
3. f(x)=54x+3/8
4. f(x)=4.5x+3/8
4? Already tried 1 but was incorrect.
it is option 2: f(x)=3/8x+54 for anyone looking this up later
To determine the correct function that represents the total number of inches the caterpillar crawls after x minutes, let's break down the problem step by step.
First, we know that the caterpillar crawls upwards 3/8 of an inch every minute. Therefore, after x minutes, the caterpillar would have crawled (3/8) × x inches.
Next, we know that the caterpillar was already 4.5 feet off the ground when the students began observing. Since there are 12 inches in 1 foot, the caterpillar was 4.5 × 12 = 54 inches off the ground at the beginning.
Therefore, the total number of inches the caterpillar crawls after x minutes is given by the equation: f(x) = (3/8)x + 54.
Based on the available options:
1. f(x) = (3/8)x + 4.5: This equation incorrectly starts with 4.5 inches instead of 54 inches.
2. f(x) = (3/8)x + 54: This equation is correct and matches our calculated equation.
3. f(x) = 54x + 3/8: This equation incorrectly multiplies x by 54 instead of adding 54 to the (3/8)x term.
4. f(x) = 4.5x + 3/8: This equation incorrectly starts with 4.5 inches instead of 54 inches and also multiplies x by 4.5 instead of adding 54.
Therefore, the correct function that represents the total number of inches the caterpillar crawls after x minutes is: f(x) = (3/8)x + 54.
The correct answer is option 2.
first off, how many inches in 4.5 feet?
That's the starting point.