10
advanced-math

The function f(x)=10(1.2)x+5f(x) = 10(1.2)^x + 5 models water level in a tank. What is the minimum water level?

A

5 units

B

10 units

C

15 units

D

0 units

Correct Answer: A

Choice A is the correct answer. Find the lower bound.

  1. Growth Function: 1.2>11.2 > 1 means increasing.
  2. As xx \to -\infty: (1.2)x0(1.2)^x \to 0, so f(x)0+5=5f(x) \to 0 + 5 = 5.
  3. Minimum: Approaches but never reaches 5 (horizontal asymptote).
  4. Conclusion: Minimum level is 5 units (approached but not achieved).

💡 Strategic Tip: For growth with vertical shift +k+k, minimum is kk (as xx \to -\infty).

Choice B is incorrect because 10 is the coefficient, not the minimum. Choice C is incorrect because this is f(0)=10+5f(0) = 10 + 5, not the minimum. Choice D is incorrect because the +5 shift prevents reaching 0.