Which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? Explain your reasoning.

According to the rule of 72,
72/rate=time
72÷9.6=7.5 years

An alternative method for resolution using the main formula
2300=1150(1+0.096/4)^4t
Isolate t
t=((log(2,300÷1,150)÷log(1+(0.096÷4))÷4))=7.31 years

I hope this is helpful:-)

Response:

If there are "p" pounds of peanuts and "m" pounds of a mixture containing '20% peanuts and 80% almonds', then we can formulate the following equations:

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

The solution yields 5 lb peanuts and 5 lb mixture.

Detailed explanation:

In the mixture that Delaney desires to create, there will be

lb

= 6 lb of peanuts

Thus, there will be (10 - 6) lb

= 4 lb of almonds

If Delaney has "p" pounds of peanuts and "m" pounds of the '20% peanuts and 80% almonds' mixture, then based on the problem statement,

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

From equation (2), we derive

m = 5 --------------(3)

From (1) and (3), we find that

p = (10 - 5) = 5

To start, we will shift the non-repeating segment of the decimal to the left side by dividing by a power of 10.

Then we will assign a variable to represent the value and also shift the repeating segment to the left.

Essentially, the concept here is that we can denote the repeating portion with a variable, let's say "x", and move forward with the calculation;





you can verify that using your calculator.

The function is applicable within the segments of x:
(-∞, -1) and [-1, 7), meaning it is valid for x < 7.

Importantly,
the function cannot be evaluated at x = -1 in the left part of the linear graph, while it is valid at x = -1 in the right segment of the same line. Additionally, the function is not defined at x = 7 or any value above it.

Conclusion: x < 7.

Detailed analysis:

The scenario mentions that a mouse covered a total of 3/24 miles over a span of 3 hours. The mouse traveled an identical distance during each hour. To find out how far the mouse went in one hour, we need to divide 3/24 miles by 3. Thus,

Matt's calculation indicates that the outcome is 3/8 hours. When he divides 3/24 by 3, he should take the reciprocal of 3, but he doesn't, resulting in 9 as the numerator and 24 as the denominator. The fraction 9/24 simplifies to 3/8. However, the accurate answer should have been 1/24 hours.