We have been given that you invest $850 into a stock market fund, which grows at a rate of approximately 4% each year. We are asked to write an equation that can be used to calculate the amount of money in the fund after x years.
We will use exponential growth formula to solve our given problem.
An exponential function is in form
, where,
y = Final amount,
a = Initial amount,
r = Growth rate in decimal form,
x = Time.
Let us convert 4% into decimal.
.
We have
and
, so our equation would be:
![y=850\cdot (1+0.04)^x](https://tex.z-dn.net/?f=y%3D850%5Ccdot%20%281%2B0.04%29%5Ex)
![y=850\cdot (1.04)^x](https://tex.z-dn.net/?f=y%3D850%5Ccdot%20%281.04%29%5Ex)
Therefore, the equation
can be used to calculate the amount of money in the fund after x years.
Answer:
Alan: 200 m/min
Brian: 150 m/min
Step-by-step explanation:
Given : Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same point. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes.
To find : What are their rates, in meters per minute?
Solution :
Let n represent the number of laps that Alan completes in 9 minutes.
Then n-1 is the number of laps Brian completes.
45 seconds = 3/4 minutes.
The difference in their lap times in minutes per lap is
![\frac{9}{(n -1)}-\frac{9}{n} =\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B%28n%20-1%29%7D-%5Cfrac%7B9%7D%7Bn%7D%20%3D%5Cfrac%7B3%7D%7B4%7D)
Solving the equation we get,
![\frac{9n-9n+9}{n(n -1)} =\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B9n-9n%2B9%7D%7Bn%28n%20-1%29%7D%20%3D%5Cfrac%7B3%7D%7B4%7D)
![9\times 4=3\times n(n -1)](https://tex.z-dn.net/?f=9%5Ctimes%204%3D3%5Ctimes%20n%28n%20-1%29)
![36=3\times n(n -1)](https://tex.z-dn.net/?f=36%3D3%5Ctimes%20n%28n%20-1%29)
![n^2-n-12=0](https://tex.z-dn.net/?f=n%5E2-n-12%3D0)
![n^2-4n+3n-12=0](https://tex.z-dn.net/?f=n%5E2-4n%2B3n-12%3D0)
![n(n-4)+3(n-4)=0](https://tex.z-dn.net/?f=n%28n-4%29%2B3%28n-4%29%3D0)
![(n-4)(n+3)=0](https://tex.z-dn.net/?f=%28n-4%29%28n%2B3%29%3D0)
![n=4,-3](https://tex.z-dn.net/?f=n%3D4%2C-3)
Neglecting n=-3
So, n=4
Then Alan's speed in m/min is
![S=\frac{D}{T}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7BD%7D%7BT%7D)
![S_a=\frac{4\times 450}{9}](https://tex.z-dn.net/?f=S_a%3D%5Cfrac%7B4%5Ctimes%20450%7D%7B9%7D)
![S_a=200 m/min](https://tex.z-dn.net/?f=S_a%3D200%20m%2Fmin)
Brian completes 3 laps in that 9-minute time, so his rate is
![S_b=\frac{3\times 450}{9}](https://tex.z-dn.net/?f=S_b%3D%5Cfrac%7B3%5Ctimes%20450%7D%7B9%7D)
![S_b=150 m/min](https://tex.z-dn.net/?f=S_b%3D150%20m%2Fmin)
Therefore, Alan: 200 m/min
Brian: 150 m/min
Answer:
6/r + 5
Step-by-step explanation:
Hello : here is a solution
What we have been given here are two points.
f(3) = -4 is the same as (3, -4)
f(2) = 6 is the same as (2, 6)
We can then use these two points to find the equation of a line.
Step 1: Find the slope
Slope Formula: (y2 - y1) / (x2 - x1)
Slope = (6 - - 4) / (2 - 3) = (10) / (-1) = -10
Step 2: Find the y-intercept
To find the y-intercept, we'll take our slope and one of our points and plug them into slope-intercept form, then solve for b.
Slope-Intercept Form: y = mx + b
Point = (2, 6)
6 = 2(-10) + b
6 = -20 + b
b = 26
Step 3: Create the equation of the line
Now that we have the slope and y-intercept, all that's left to do is plug both of those values into slope-intercept form.
y = -10x + 26
Answer: y = -10x + 26
Hope this helps!