ACT (Enhanced)MathematicsEasy
A botanist is tracking the growth of a rare plant species. The height of the plant, h(t), in centimeters, after t weeks, can be modeled by the function h(t) = 3 * (1.2)^t. What is the initial height of the plant when t = 0?
- A1.2 cm
- B3 cm
- C3.6 cm
- D0 cm
Show answer & explanationAnswer & explanation
Correct answer: B. 3 cm
The initial height of the plant occurs at time t=0. Substituting t=0 into the given exponential function directly yields the initial value.
Why the other options are wrong
- A. This is the growth factor, not the initial height.
- C. This would be the height after one week, not the initial height.
- D. This would imply the plant had no height initially, which is incorrect for the given function.
Initial Value of Exponential Function
The initial value of an exponential function f(x) = a * b^x is the value of 'a', which represents the output when x = 0.
- In f(x) = a * b^x, 'a' is the initial value.
- It's the y-intercept of the exponential curve.
- Represents the quantity at the start (e.g., time t=0).
Memory trick: Always Start with 'A' for the Amount at the start.