Set 15: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Find when coverage goes from 5% to 100%. 1. Growth Needed: $\frac{100}{5} = 20$ times larger. 2. Doublings: $20\approx 2^4 = 16$ (close) to $2^5 = 32$. Actually $20$ is between $2^4=16$ and $2^5=32$, closer to $2^{4.32}$. 3. Time: About 4-5 doublings $\times$ 3 days = 12-15 days. 4. More precise: $2^x = 20$, so $x \approx 4.32$ doublings, thus $4.32\times 3 \approx 13$ days. Strategic Tip: To grow by factor of 20, need $\log_2(20) \approx 4.32$ doublings. Choice B is incorrect because doubling is much faster. Choice C is incorrect because this assumes 10 doublings. Choice D is incorrect because this doesn't match the calculation.