Math multiple choice
2 answers:
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Answer:
a. Decay
b. 0.5
c. 4
Explanation:
If we have a function of the form
then
a = intital amount
b = growth / decay rate factor
x = time interval
If b > 1; then the equation is modelling growth. If b < 0, then the equation is modelling decay.
Now in our case, we have
Here we see that
inital amount = a = 4
b = 1/ 2 < 0, meaning the function is modeling decay
decay factor = b = 1/2
Therefore, the answers are
a. Decay
b. 0.5
c. 4
The two containers hold 328 ounces at the they hold same amount of water.
<u>Step-by-step explanation:</u>
The equations below model the ounces of water, y, in each container after x minutes.
At the time after the start when the containers hold the same amount of water, the two equations must be equal.
⇒
The first step is to divide everything by 2 to make it simplified.
⇒
Now put everything on the left .
Add the like terms together to further reduce the equation
Factorizing the equation to find the roots of the equation.
Here, b = -12 and c = -28
where,
- b is the sum of the roots ⇒ -14 + 2 = -12
- c is the product of the roots ⇒ -14 × 2 = -28
- Therefore, (x-14) (x+2) = 0
- The solution is x = -2 or x = 14
Take x = 14 and substitute in any of the given two equations,
⇒
⇒
⇒ 328 ounces
∴ The two containers hold 328 ounces at the they hold same amount of water.