What is the domain of the function y=sqrt x+4

Domain: set of all numbers that can be inputted into a function

Since you cannot take the square root of a negative number, this means that x-4 CANNOT be negative. So it's either 0 or it's positive.

So.. x−4≥0

x−4+4≥0+4

x≥4

So this says: "Any number greater than or equal to 4 will result in x-4 being either 0 or some positive number"

So this means that the domain is

{x|x≥4}

This basically says: "the domain is the set of all numbers x such that x is greater than or equal to 4"

In interval notation, the domain is [4,∞)

The range is the set of all possible outputs. We can find the most extreme point of the range by plugging in the most extreme value for the domain

sqrt(x-4) = sqrt(4-4) = sqrt(0) = 0

So the smallest possible output is y=0, which means that the range is

{y|y≥0}

This basically says: "the range is the set of all numbers y such that y is greater than or equal to 0"

In interval notation, the range is

[0,∞)

It would take 0.8 years longer for Faith's money to double than for Kevin's money to double.

Step-by-step explanation:

We are to find the time it would take for each person's money to double and we would be making use of compound interest formula to solve for this

For Faith

Faith invested $350 in an account paying an interest rate of 4 5/8% compounded monthly.

Double $350 = $700

Interest rate = 4 5/8%

= 4.625%

First, convert R as a percent to r as a decimal

r = R/100

r = 4.625/100

r = 0.04625 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(700.00/350.00) / ( 12 × [ln(1 + 0.04625/12)] )

t = ln(700.00/350.00) / ( 12 × [ln(1 + 0.003854167)] )

t = 15.016 years

Therefore, it would take 15.016 years for Faith's money to double

For Kelvin

Double $350 = $700

Kevin invested $350 in an account paying an interest rate of 4 7/8% compounded continuously.

Interest rate = 4.875%

First, convert R as a percent to r as a decimal

r = R/100

r = 4.875/100

r = 0.04875 per year,

Then, solve the equation for t

t = ln(A/P) / r

t = ln(700.00/350.00) / 0.04875

t = 14.218 years

Therefore, it would take 14.218 years for Kelvin's money to double.

To the nearest hundredth of a year, how longer would it take for Faith's money to double than for Kevin's money to double is calculated as

15.016 years - 14.218 years

= 0.798 years

Approximately to the nearest hundredth ≈ 0.80 years

Therefore, it would 0.8 years longer for Faith's money to double than for Kevin's money to double.