6
advanced-math

For h(x)=15(1.08)xh(x) = 15(1.08)^x, approximately how many times larger is h(20)h(20) than h(10)h(10)?

A

About 2.2 times

B

About 10 times

C

About 1.08 times

D

Exactly 2 times

Correct Answer: A

Choice A is the correct answer. Calculate the ratio.

  1. Ratio: h(20)h(10)=15(1.08)2015(1.08)10=(1.08)10\frac{h(20)}{h(10)} = \frac{15(1.08)^{20}}{15(1.08)^{10}} = (1.08)^{10}.
  2. Estimate: (1.08)102.162.2(1.08)^{10} \approx 2.16 \approx 2.2.
  3. Conclusion: h(20)h(20) is about 2.2 times larger.

💡 Strategic Tip: For ratios, factors divide out, leaving a power of the base.

Choice B is incorrect because the difference in inputs (10) is not the multiplication factor. Choice C is incorrect because this is just one step, not 10 steps. Choice D is incorrect because(1.08)10eq2(1.08)^{10} eq 2 exactly.