ACT (Enhanced)MathematicsEasy
A scientist is studying the growth of a certain type of mold. The area covered by the mold, A, in square centimeters, can be modeled by the function A(t) = 5 * (1.5)^t, where t is the time in hours. What is the initial area covered by the mold when t = 0?
- A7.5 cm²
- B0 cm²
- C5 cm²
- D1.5 cm²
Show answer & explanationAnswer & explanation
Correct answer: C. 5 cm²
The initial area corresponds to the time t = 0. Substitute t = 0 into the function: A(0) = 5 * (1.5)^0. Any non-zero number raised to the power of 0 is 1. So, A(0) = 5 * 1 = 5 cm².
Why the other options are wrong
- A. This would be A(1), the area after 1 hour.
- B. This would mean no mold initially, which contradicts the function form.
- D. This is the growth factor, not the initial amount.
Exponential Function Initial Value
For an exponential function of the form y = ab^x or y = ae^(kx), the initial value (when x=0) is represented by 'a', because b^0 = 1 and e^0 = 1.
- The 'a' term is the y-intercept.
- Represents the starting quantity or amount.
- Any non-zero number to the power of zero is one.
Memory trick: A is for 'At start', B is for 'By how much it changes'.