<h3>
Answer: B) 1.0 year</h3>
===========================================================
Explanation:
We have these two functions
- f(t) = 12(1.02)^(4t)
- g(t) = 12(1.09)t
which represent the amounts for his friend and William in that order. Strangely your teacher mentions William first, but then swaps the order when listing the exponential function as the first. This might be slightly confusing.
The table of values is shown below. We have t represent the number of years and t starts at 0.5. It increments by 0.1
The f(t) and g(t) columns represent the outputs for those mentioned values of t. For example, if t = 0.5 years (aka 6 months) then f(t) = 12.48 and that indicates his friend has 12,480 dollars in the account.
I've added a fourth column labeled |f - g| which represents the absolute value of the difference of the f and g columns. If f = g, then f-g = 0. The goal is to see if we get 0 in this column or try to get as close as possible. This occurs when we get 0.09 when t = 1.0
So we don't exactly get f(t) and g(t) perfectly equal, but they get very close when t = 1.0
It turns out that the more accurate solution is roughly t = 0.9925 which is close enough. I used a graphing calculator to find this approximate solution.
It takes about a year for the two accounts to have the same approximate amount of money.
Answer:
1 mi/hr
Step-by-step explanation:
Given that:
Speed in still water, s = 5 mi/hr
Let speed of current = x
Time = distance /speed
Upstream (subtract speed of current) = 5 - x
Upstream time = 8 / 5 - x - - - (1)
Downstream (add speed of current) = 5 + x
Downstream time = 12 / 5 + x - - - (2)
Equate (1) and (2)
8 / (5 - x) = 12/ (5 + x)
8(5 + x) = 12(5-x)
40 + 8x = 60 - 12x
40 - 60 = - 12x - 8x
-20 = - 20x
x = 1
Spwed of current = 1 mi/hr
Answer:
-5/14
Step-by-step explanation:
When adding fractions, you need to have a common denominator, the bottom part of a fraction. Because one denominator is 14 and the other is 7, you must create a new denominator.
To create a new denominator, you can either reduce a fraction or multiply it by something, which is easier.
For this problem, we can convert 2/7's denominator into 14 instead of 7 by multiplying the fraction by 2/2:
<u>2</u> x <u>2</u> = <u>4</u>
7 2 = 14
2/7 has now converted into 4/14. Now, we can easily add.
-9/14+4/14 This can be rewritten as something more understandable.
4/14-9/14 We are now subtracting.
-5/14 This cannot reduce, so it is our answer.
I hope this helps!! Have an amazing day and let me know if you want more explanation ;)
Answer:
100 people
Step-by-step explanation:
<em>Population</em><em> </em><em>Of</em><em> </em><em>People</em><em>=</em><em>1</em><em>1</em><em>5</em><em>Percentage</em><em>ncrease</em><em>=</em><em>1</em><em>5</em><em>%</em>
<em>The</em><em> </em><em>New</em><em> </em><em>Population </em><em>corresponds </em><em>to</em><em> </em><em>1</em><em>1</em><em>5</em><em>%</em>
<em>(</em><em>That</em><em> </em><em>is</em><em> </em><em>1</em><em>0</em><em>0</em><em>+</em><em>1</em><em>5</em><em>)</em>
<em>We</em><em> </em><em>want</em><em> </em><em>to </em><em>find</em><em> </em><em>the</em><em> </em><em>popula</em><em>tion</em><em> </em><em>that</em><em> </em><em>corresponds</em><em> </em><em>to </em><em>100%</em><em> </em><em>that </em><em>is </em><em>the</em><em> </em><em>original</em><em> </em><em>population</em><em>.</em>
<em>Therefore</em><em> </em><em>Original </em><em>Population</em><em>;</em>
<em>
</em>
<em>
</em>
the answer is G
Step-by-step explanation:
G is the answer
