Answer:
21. y = 75000·0.935^t
22. after 74.6 days
23. y = 27.8112·1.18832^t
24. 18.8% per month
25. 1748
Step-by-step explanation:
22. It is convenient to use the graphing calculator to solve this problem. The number of days is where the exponential curve has the value 500. It is about 74.55 days. (see the first attachment)
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23. y = 27.8112·1.18832^t (see the second attachment)
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24. The rate of change is the difference between the base of the exponential and 1, often expressed as a percentage. The time period is the units of t.
(1.18832 -1) × 100% ≈ 18.8% . . . . per month
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25. Evaluating the function for t=24 gives y ≈ 1748.30425259 ≈ 1748.
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<em>Comment on graphing calculator</em>
A graphing calculator can make very short work of problems like these. It is worthwhile to get to know how to use one well.
This problem can take a while if you cannot observer the answer quickly.
First of all we can see that 32=2*2*2*2*2=2^5
243, if you don't know its actually is 3^5
Now we can see that this turns into...
- 2^5/3^5
since the 5th power doesn't change the sign of the original number, we can put the negative in the ( ), if you don't know what I mean look below
(-3)^2=9 Positive
(-3)^3=-27 Negative since its to the odd power it keeps the sign.
This problem can be simplified to.
(-2/3)^5
And this is the answer :D
If you have any questions just put them in the comments.
Answer:
5 2/3 hours
Step-by-step explanation:
We can use a ratio to solve this problem
hours over money
4.5 hours x hours
------------- = ------------
27 dollars 34 dollars
Using cross products
4.5 * 34 = 27 * x
153 =27x
Divide each side by 27
153/27 = 27x/27
5.666666 hours
The pattern starts at 2/14 and increases by 1/14 each node, so the next fraction is 6/14 which simplifies into 3/7
2a
tan37=r/8
r=8tan37
r≈6 in rise per step (to nearest whole inch)
2b
11*12/6=22 steps needed to climb the 11 ft to the entrance
...
3a
tanα=14/20
α=arctan(7/10)
α≈35° (to nearest whole degree)
..
3b
tanα=21/17
α=arctan(21/17)
α≈51° (to nearest degree)
