Unit 3 Review Extra Key

EXTRA PRACTICE-KEY P_{n} = P[(1 - (1 + i) ^ (- n))/i] Jeremy purchased a house for $257,000. He paid a 15% down payment. He gets a 25 year mortgage with an interest rate of 5.25% 13 How much was his down payment? 257000(0.15) +6 38,550 2) How much of the house is financed? 257000 - 38550 = 6217, 450 33 What is his monthly payment for principal and interest? 91y + 50 + \mathfrak{P}[(1 - (1 + 515/12) ^ - 200)/(525/12)] 318450 AN5 =P 71.309. O*L_{e} =P/ 4) How (1309.06)(300) +38,550= boxed \$431,268 5) How much interest will he pay over the life of the loan? (1304.06)(300) - 217450 + boxed 417,268 ) Solve. Round to 3 decimal places (where appropriate). Remember to check for extraneous solutions when given a log equation. Ain on one side change to 6) lim 2 x = 3 2 exponential form e ^ (3/2) = x X \approx 4.482 Ain on both sides condenses cancel 7) Inx-in-in ln(x/(2 ^ 3)) = ln(9 ^ (1/2)) x/8 = 3 x = 24 #leg en one side, isolak, then change to exponential form 8) 3 * log(4x) = 13/5 log_2(4x) = 4 2 ^ 4 = 4x 16 = 4x 4 = x *xs in exponent, ise lak base (if nexted!) & then take kiyor in of both sides 91 5e ^ (5a) = 10/5 epsilon ^ (5x) = 2 ln(e ^ (5x)) = ln(2) 5 * 1ne = ln(2) 5x = underline ln^ 2 x = 0.139 12( x ^ (2pi) = x ^ (2 ^ 2 - 4) some concel 2x = x ^ 2 - 8 0 = x ^ 2 - 2x - 8 ! 0 = (x - 4)(x + 2) x = 4, - 2 15) 123 *x's in the exponent, take log of both sides, log(12 ^ (x - 4)) = log(3 ^ (x - 2)) (x - 4) * log(12) = (x - 2) * log(3) x's on both sides X109 12-4 log12=x1093-2 log +1 log A gat x's to one sele, non-x's to x * log(l) * 2 - x * log(3) = - 2 * log(3) + 4 * log(12) x (log 12-1093)=(2 log3+4log 12)~ ≈5.585 16 g 12-log -3 (log(12) - log(3)) te must (you will not get the correct answer 1073 ^ (3 ^ 3 + 3) = 37 ^ 7 log(3 ^ (x + 2)) = log(37) (x ^ 2 + 2) * log(3) = log(37) since x is only on one side ((x ^ 2 + 2) * log(3) = log(37))/(log(3)) x ^ 2 + 2 = (log(37))/(log(3)) \\ -2 aligned 13) In(x+1) - ln(x - 2) = ln(x) *In in condense, then concel In (x + 1)/(x - 2) = ln(x) (x - 2) * (x + 1)/(x - 2) = x(x - 2) x + 1 = x ^ 2 - 2x 0 = x ^ 2 - 3x - 1 A not Guad Form x = (3 plus/minus sqrt(9 - 4(1 * (- 1))))/(2(1)) (3 plus/minus sqrt(13))/2 = (f + (13))/2 \approx 3.303 (3sqrt(13))/2 = - 303 x \approx 3.303 #legon one sida, Change in exponential change in fructen 11)( o*g_{6} * 15 * 0.6 x ^ 0.6 = 15 X ^ (9/5) = 15 x ^ 2 = (lec * 37)/(log(3)) - 2 X = plus/minus sqrt((log(37))/(log(3))) - 2 x = plus/minus 1.134 reciprocial exponent (x ^ 75) ^ (1/3) = (15) ^ (15/3) x \approx 91.233 14) lomix logsfx-81-2 log on one side, condense, when change to expp form log_3(x) * (x - 8) = 2 3 ^ 2 = x ^ 2 - 8x 0 = x ^ 2 - 8x - 9 0 = (x - 9)(x + 1) x = 9, - 1 x = 9 A