Joe bought an apple tree that was 48 inches in height. He noticed that this tree grew approximately 4 inches in height each year.
Which statement best describes the function that could be used to model the height of the apple tree, h(t), as a function of time, t, in years.
1. The height of the apple tree can be represented by a linear function, and the variable t is multiplied by 4 in the equation representing the function.
2. The height of the apple tree can be represented by an exponential function, and the variable t is multiplied by 4 in the equation representing the function.
3. The height of the apple tree can be represented by a linear function, and the variable t is an exponent in the equation representing the function.
4. The height of the apple tree can be represented by an exponential function, and the variable t is an exponent in the equation representing the function.
Disagree, 1, not an exponent.
I feel like its 3 but idk?
The correct answer is:
4. The height of the apple tree can be represented by an exponential function, and the variable t is an exponent in the equation representing the function.
Explanation:
Since the tree grows approximately 4 inches in height each year, this indicates exponential growth. In an exponential function, the independent variable (t) is typically the exponent. Therefore, the height of the apple tree (h(t)) can be modeled by an exponential function.
To answer this question, we need to understand the growth pattern of the apple tree over time.
The information given states that the tree grew approximately 4 inches in height each year. Since the growth is constant, this suggests a linear relationship between the height of the tree and the time in years.
Therefore, the function that could be used to model the height of the apple tree, h(t), as a function of time, t, in years would be a linear function.
Option 1 correctly describes the situation, stating that the height of the apple tree can be represented by a linear function, and the variable t is multiplied by 4 in the equation representing the function.
So, the correct answer is option 1: The height of the apple tree can be represented by a linear function, and the variable t is multiplied by 4 in the equation representing the function.