Answer:
(See attached graph)
Step-by-step explanation:
To solve a second-order homogeneous differential equation, we need to substitute each term with the auxiliary equation 
where the values of 
are the roots:
Since the values of are equal real roots, then the general solution is 
.
Thus, the general solution for our given differential equation is 
.
To account for both initial conditions, take the derivative of 
, thus, 
Now, we can create our system of equations given our initial conditions:
We then solve the system of equations, which becomes easy since we already know that 
:
Thus, our final solution is:
8 1/2 = 8.5
10 3/4 = 10.75
9 3/4 = 9.75
8.5 + 10.75 + 9.75 = 29 inches in total <==
<u>Given</u>:
Given that in a game a player draws and replaces a card from a deck 2 times.
The possible outcomes and payouts are given.
We need to determine the expected value for someone playing the game.
<u>Expected value:</u>
The expected value for someone playing the game can be determined by
Simplifying the values, we have;
Dividing the terms, we get;
Adding, we have;
Thus, the expected value for someone playing the game is $8
Answers:
- a = 475
- r = -0.5
- f(3) = 59.4
=======================================================
Explanation:
Any exponential function is of the form y = a*b^x
Comparing that to y = 475*(0.5)^x, we see that a = 475 and b = 0.5
Set b equal to 1+r and solve for r
1+r = 0.5
r = 0.5-1
r = -0.5
The negative r value tells us that the growth rate is -50%, in other words, we have a 50% decay rate. The amount drops by 50% each time x goes up by 1. This is the same as saying the amount cuts in half each time x goes up by 1.
-----------------------
Lastly, plug in x = 3 to find f(3)
f(x) = 475(0.5)^x
f(3) = 475(0.5)^3
f(3) = 59.375
f(3) = 59.4
