Current amount in account
P=36948.61
Future value of this amount after n years at i=11% annual interest
F1=P(1+i)^n
=36948.61(1.11)^n
Future value of $3000 annual deposits after n years at i=11%
F2=A((1+i)^n-1)/i
=3000(1.11^n-1)/0.11
We'd like to have F1+F2=280000, so forming following equation:
F1+F2=280000
=>
36948.61(1.11)^n+3000(1.11^n-1)/0.11=280000
We can solve this by trial and error.
The rule of 72 tells us that money at 11% deposited will double in 72/11=6.5 years, approximately.
The initial amount of 36948.61 will become 4 times as much in 13 years, equal to approximately 147800 by then.
Meanwhile the 3000 a year for 13 years has a total of 39000. It will only grow about half as fast, namely doubling in about 13 years, or worth 78000.
Future value at 13 years = 147800+78000=225800.
That will take approximately 2 more years, or 225800*1.11^2=278000.
So our first guess is 15 years, and calculate the target amount
=36948.61(1.11)^15+3000(1.11^15-1)/0.11
=280000.01, right on.
So it takes 15.00 years to reach the goal of 280000 years.
Answer:
When you set the function equal to zero, the solution is x = 3; therefore, the graph has an x-intercept at x = 3.
Step-by-step explanation:
The given function is 
.
So, for real zeros and x-intercept, the y-coordinate must be equal to zero.
Then it becomes 
⇒ x - 2 = 1 {Since log 1 = 0}
⇒ x = 3
Therefore, when you set the function equal to zero, the solution is x = 3; therefore, the graph has an x-intercept at x = 3. (Answer)
Answer: 20.57142857
Step-by-step explanation:
148 = 3x + 3 + 4x + 1
Step one: combine like terms
148 = 7x + 4
Step 2: Subtract the 4 over to 148
144 = 7x
Step 3: Divide 7 on both sides
20.57142857 = x
Well, we can be sure that whatever the width is, we can call it ' W '. Then, from information in the question, the length of the garden is ' 3W '.
Now, the perimeter of a rectangle is (length + width + length + width). Using the fancy algebra labels I just gave them, that's (3W + W + 3W + W). And now I can go through that, add up all the Ws, and get a total of 8W for the perimeter.
But he question tells us that the perimeter is 24 yards, so 8W = 24 yds.
Divide each side of that equation by 8, and we discover that W = 3 yds. And if THAT's true, then 3W = 9 yds. Bada bing ! We have the dimensions of the garden.
It's 3 yards wide and 9 yards long.
Answer:
209/10
Step-by-step explanation:
