course Mth 173
I am still having problems with 17-20. I just don't know how to start the equations.
1.5000 x 1.05 = 52505250 x 1.05 = 5512.50
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5512.50 x 1.05 = 5788.13
5788.13 x 1.05 = 6077.54
5000 x (1.05 ^ 100) = 657506.29
2. 500 x 1.12 = 560.00
560 x 1.12 = 627.20
627.20 x 1.12 = 702.46
702.46 x 1.12 = 786.76
.12
3. P0 x (1.06 ^ 100)
4. GR - .15 GF ?1.15 500 x (1.15 ^ 20)
GR - .07 GF ?1.07 30000 x (1.07 ^ 30)
GR - .05 GF ?1.05 2000 x (1.05 ^ 40)
5. GR - .10 GF ?1.10
200 x (1.10 ^ t)
200 x (1.10 ^ 0) = 200
200 x (1.10 ^ 5) = 322.10
200 x (1.10 ^ 10) = 518.75
200 x (1.10 ^ 20) = 1345.50
7.28 years
4.27 years
$600 ?11.53 years
$672.75 ?12.73 years
6. 200 x (1.20 ^ 3.805) = 400
It takes almost half the time with double the interest rate.
7. 7.26 years ?It takes almost the same amount of years to make $2000 instead of $200 by putting more money at first (principle).
8. 1 x (1.10 ^ 1) = 1.10
1.10 x (1.20 ^ 1) = 1.32
1.32 x (1.30 ^ 1) = 1.72
1.72 x (1.40 ^ 1) = 2.41
The final principal does not increase by the same amount with each rate increase, it increases just like the rate.
At 10% = approximately 7.5 years
At 20% = approximately 4 years
At 30% = approximately 2.7 years
At 40% = approximately 2.1 years
The doubling time does not change by a consistent amount.
9. 5 x (1.10 ^ 1) = 5.50
5.50 x (1.20 ^ 1) = 6.60
6.60 x (1.30 ^ 1) = 8.58
8.58 x (1.40 ^ 1) = 12.01
The final principal does not increase by the same amount with each rate increase, it increases just like the rate.
At 10% = approximately 7.25 years
At 20% = approximately 3.85 years
At 30% = approximately 2.65 years
At 40% = approximately 2.07 years
The doubling time does not change by a consistent amount.
10. P(?oublingTime) = $4000
$2000 x (1.10 ^ ?oublingTime) = $4000
/2000 /2000
1.10 ^ ?oublingTime = $2
11. P(2 + ?oublingTime) = 2P(2)
$5000 x (1.08^(1 + ?oublingTime)(1.08^(1 + ?oublingTime) = 10000(2)
/5000 /5000
(1.08^(1 + ?oublingTime)(1.08^(1 + ?oublingTime) = 2000(2)
(1.08^1 x 1.08^?oublingTime) (1.08^1 x 1.08^?oublingTime)=2000(2)
/1.08
(1.08^ ?oublingTime) (1.08^ ?oublingTime) = 2000(2)
12. n = 2: 2.25; .46828
n = 4: 2.44140625; .27687375
n = 10: 2.59374246; .1245375399
n = 100: 2.704813829; .0134661706
n = 1000: 2.716923932; .001356068
n = 10000: 2.718145927; 1.34073e-4
n = 100000: 2.7182; 1.17e-5
n = 1000000: 2.7183; 1.085e-6
13. My suggestion is 10,000. When I subtracted the numbers it gave me a result of 1.34. That is not correct.
14. n = 200000
15. 10 millennium = 16.00 + -.07 = 15.93; 15.93 ^ 10 = 1.05234407 e12
20 millennium = 15.93 ^ 20 = 1.107428041e24
30 millennium = 15.93 ^ 30 = 1.165395332e36
40 millennium = 15.93 ^ 40 = 1.226396866e48
50 millennium = 15.93 ^ 50 = 1.290591469e60
15.5 Q(t) = Q(0) x (.93 ^ t)
16. Q(t) = 30 mg (.85) ^ t
Q(?t) = 30 mg (.85) ^ ?t = 15 mg
30 mg (.85) ^ ?t = 15 mg
/30 /30
.85 ^ ?t = ?
17. Q(t) = 550 mg (.89) ^ t
550 mg (.89 ^ 5) = 307.1232697
Q(?t) = 550 mg (.89) ^ ?t = 275 mg
550 mg (.89) ^ ?t = 275 mg
/550 /550
.89 ^ ?t = ?
17.
18.
19.
20.
21. 2 would be the value of b in each function.
y = 12(2 ^ (-.5x))
y = 12 (.03125 ^ x)
y = .007(2 ^ (.71x))
y = .007 (1.635804117 ^ x)
y = -13 (2 ^ (3.9x))
y = -13 (14.92852786x)
22. The value of b is e or 2.718 in each function.
y = 12(e ^ (-.5x))
y = 12 (.6065621044 ^ x)
y = .007 (e ^ (.71x))
y = .007 (2.033991259 ^ x)
y = -13 (e ^ (3.9x))
y = -13 (49.40244911 ^ x)
23. k = approximate 3.7
24. k = approximate 2.57
25. (0,12) & (8, 20)
12 = A x b ^ 0
20 = A x b ^ 8
.6 = b ^ 0/b ^ 8
.6 = b ^ (-8)
.6 ^ (-1/8) = b ^ (-8) ^ (-1/8)
1.065935911 = b
12 = A x (2 ^ (0k))
20 = A x (2 ^ (8k))
.6 = [2 ^ (0k)]/[2 ^ (8k)]
.6 = 2 ^ (-8k)
26. (2, 4) & (5, 3)
4 = A x b ^ 2
3 = A x b ^ 5
1.33 = b ^ 2/b ^ 5
1.33 = b ^ (-3)
1.33 ^ (-1/3) = b ^ (-3) ^ (-1/3)
.9093186943 = b
4 = A x (2 ^ (2k))
3 = A x (2 ^ (5k))
1.33 = [2 ^ (2k)]/[2 ^ (5k)]
1.33 = 2 ^ (-3k)
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