The mathematical model representing the scenarios described can be expressed as follows :
- If n ≤ 8 ; A(n) = 31.25n
- If n > 8 ; A(n) = 31.25 + 46.875(n - 8)
1.)
Amount paid per 8 hours at summer job = 250
Additional hours beyond, 8 hours = 1.5 × hourly rate
Let:
- hourly rate = p
- Number of hours worked = n
- Amount earned as a function of n, A(n)
Hourly rate, p = (250 ÷ 8) = 31.25
Therefore, the hourly rate, p at the summer job = $31.25
Overtime pay = 1.5 × 31.25 = $46.875
Therefore,
If n ≤ 8 ; A(n) = 31.25n
If n > 8 ; A(n) = 31.25 + 46.875(n - 8)
2.)
Let :
- Number of playing hours = n
- Total amount charged as a function of n ; T(n)
Therefore,
T(n) = First hour fee + (charge per additional hour × number of additional hours)
T(n) = 15 + 5(n - 1)
Therefore, the models can be used to calculate the total earning and amount charged for any given hour value.
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Answer:
-3,-1,0,5,7
Step-by-step explanation:
3/5+1/4=17/20
12/20+5/20=17/20
Answer:
Quadratic functions are those where their rate of change changes at a constant rate. Exponential functions are those where their rate of change is proportional to itself.
An example of a quadratic function would be the shape that a ball makes when you throw it. Gravity causes a constant acceleration, the ball slows down as it is moving up, and then it speeds up as it comes down.
An example of an exponential function would be the population of a bacterium as long as there is enough space and nutrients or how your money grows with compound interest in a bank.
A quadratic function is one in the form
f(x)=ax2+bx+c
It’s rate of change (first derivative) is linear.
f′(x)=2ax+b
The rate of the rate of change (second derivative) is constant.
f′′(x)=2a
Quadratics are then the solutions to the differential equation
f′′=C
An exponential function is one in the following form.
g(x)=Aekx
It’s rate of change is another exponential function.
g′(x)=Akekx
So exponentials are the solutions to the differential equation
g′=kg
Step-by-step explanation:
Yes. : )
