Answer:
Part 38)

Part 39)

Part 45) The system has infinity solutions
Part 47) Is a exponential growth, the percent rate of change is 20%
Part 48) Is a exponential decay, the percent rate of change is -60%
Explanation:
Part 38) Write an equation in point slope form of the line that pass through the given points
step 1
Find the slope
The formula to calculate the slope between two points is equal to

we have
(1,3) and (-3,0)
substitute



step 2
Find the equation in point slope form

we have


substitute

Part 39) Write an equation in point slope form of the line that pass through the given points
step 1
Find the slope
The formula to calculate the slope between two points is equal to

we have
(-2,-5) and (4,-1)
substitute



step 2
Find the equation in point slope form

we have


substitute

Part 45) Solve the system of linear equations using any method
----> equation A
----> equation B
Multiply the equation A by -2 both sides

-----> equation C
Compare equation B and equation C
Line B and Line C are the same line
so
The system has infinity solutions
Is a consistent dependent system
Part 47) Determine whether the function represent exponential growth or exponential decay. Identify the percent rate of change
we have

This is a exponential function of the form

where
a is the initial value or y-intercept
b is the base of the exponential function
r is the percent rate of change
b=(1+r)
If b < 1 ---> the function is a exponential decay
If b > 1 ---> the function is a exponential growth
In this problem we have

----> is a exponential growth

convert to percentage

Part 48) Determine whether the function represent exponential growth or exponential decay. Identify the percent rate of change
we have

This is a exponential function of the form

where
a is the initial value or y-intercept
b is the base of the exponential function
r is the percent rate of change
b=(1+r)
If b < 1 ---> the function is a exponential decay
If b > 1 ---> the function is a exponential growth
In this problem we have

----> is a exponential decay
--->is negative because is a decreasing function
convert to percentage
