l LCALCULUS MATH 1113 TEST 2, PART 2 (40%) Please show all your work! Answers wi

Question

l LCALCULUS MATH 1113 TEST 2, PART 2 (40%) Please show all your work! Answers without supporting work will not be given credit. Write answers in spaces provided. Each problem is worth points! 1. Solve the following equations. a) log2(x-1) log2(x +6) log2(-2) log2(x +3) b) loga(2 +x) log1y3( 2. Solve the following equations. a) 2 (49) 11 (7) +5-0 b) 4z-10 (4-*) = 3 3. John will be buying a used car for $15,000 in 3 years. How much money should he ask his parents for ow so that, if he invests it at a) 5% compounded continuously, he will have enough to buy the car? b) 5% compounded nnonthly, he will have enough to buy the car? 1r 4. The population of a colony of mosquitoes obeys the exponential growth rule. (a) If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 3 days? (b) How long is it until there are 10,000 mosquitoes?

Explanation / Answer

3) compunded continuously

15000 = P e^(.05 *3)

P = 12911

so, he maust ask $ 12911 at 5% compunded continuously

b) compunded monthly

15000 = P ( 1 + .05/ 12 )^3*12

P = 15000/1.1615

P = 12914.3

so, he must ask for $ 12914.3 at 5% compounded monthly

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