GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A botanist is studying the growth of a plant. The height of the plant, h, in centimeters, over time, t, in weeks, is modeled by the function h(t) = 3t + 15. What is the initial height of the plant?
- A15 cm
- B18 cm
- C5 cm
- D3 cm
Show answer & explanationAnswer & explanation
Correct answer: A. 15 cm
The initial height of the plant occurs at time t=0. Substituting t=0 into the function: h(0) = 3(0) + 15 = 0 + 15 = 15 cm.
Why the other options are wrong
- B. This would be the height after one week, not the initial height.
- C. This value is not directly represented in the equation as initial height.
- D. This is the growth rate per week, not the initial height.
Interpreting Linear Functions (Initial Value)
For a linear function in the form y = mx + b, 'b' represents the y-intercept, which is the initial value or starting point when x=0.
- The 'b' term in y = mx + b is the initial value.
- The initial value occurs when the independent variable (x or t) is zero.
- It represents the starting amount or condition before any change occurs.
Memory trick: The 'b' in mx+b is where you 'Begin'!