Identify the function that is exponential
1 answer:
You might be interested in
Step-by-step explanation: Our first task in this problem is to setup variables representing <em>length</em> and <em>width</em> and we do that by using the second sentence.
<em><u>The length is twice the width</u></em>
So if we call our width <em>x</em>, that means that our length is 2 times <em>x</em> or 2x
Width of the rectangle ⇒ <em>x</em>
Length of the rectangle ⇒ <em>2x</em>
Before moving on, go ahead and draw a picture of your
rectangle so that you can visualize what's going on.
I have done this for you below.
We label our widths <em>x</em> and our lengths <em>2x</em>.
Now we can use the first sentence to setup our equation.
The perimeter of a rectangle is the distance
around the outside of the figure.
So if our perimeter is 60, that means that x + x + 2x + 2x = 60.
Simplifying by combining like terms, we get 6x = 60.
Now dividing both sides by 6, we find that <em>x = 10</em>.
Since <em>x</em> represents width, our width is 10.
Our length therefore with be <em>2(10)</em> or 20.
So our width is 10 and our length is 20.
Initial salary = $50,000 .
Rate of raise = 5% each year.
Therefore, each next year salary would be 105% that is 1.05 times.
5% of 50,000 = 0.05 × 50000 = 2500.
Therefore raise is $2500 each year.
According to geometric sequence first term 50000 and common ratio 1.05.
Applying geometric sequence formula
1)
2) In order to find salary in 5 years we need to plug n=5, we get
= 50000(1.21550625)
<h3>=$60775.3125.</h3>3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.
Plugging n=10, a = 50000 and r= 1.05.
= 628894.62678.
<h3>Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.</h3>