Set 10: Exponential Functions

Choice A is correct. Choice A is the correct answer. Use the initial condition to find $A$. 1. At $t=0$: $5000= \frac{50000}{1 + Ae^0} = \frac{50000}{1 + A}$. 2. Multiply: $5000(1 + A) = 50000$. 3. Divide: $1+ A = 10$. 4. Solve: $A = 9$. 5. Verify: $P(0) = \frac{50000}{1 + 9} = 5000$ ✓ Strategic Tip: Initial condition gives $P_0 = \frac{K}{1+A}$, so $A = \frac{K}{P_0} - 1$. Choice B is incorrect because this would give $P(0) = \frac{50000}{11} \approx 4545$. Choice C is incorrect because this would give $P(0) = \frac{50000}{6} \approx 8333$. Choice D is incorrect because this would give $P(0) = \frac{50000}{46} \approx 1087$.