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An insurance company charges a 35-year old non-smoker an annual premium of $118 for a $100,000 term life insurance policy. The premiums for 45-year olds and 55-year old no smokers are $218 and $563, respectively. Write a quadratic model for the premium p as a function of age a.

Respuesta :

Aliwohaish12
p=ma^2+ba+c, so you have 118=m35^2+35b+c 218=m45^2+45b+c 563=m55^2+55b+c so solving I get m=49/40 b=-88 c=13579/8 so its p=(49/40)a^2-88a+(13579/8)
isyllus

Answer:

[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]

Step-by-step explanation:

Let premium p for age of a , (p,a)

# An insurance company charges a 35-year old non-smoker an annual premium of $118 for a $100,000 term life insurance policy.

(35,118)

# An insurance company charges a 45-year old non-smoker an annual premium of $218 for a $100,000 term life insurance policy.

(45,218)

# An insurance company charges a 55-year old non-smoker an annual premium of $563 for a $100,000 term life insurance policy.

(55,563)

Let quadratic model be p=Aa²+Ba+C

Substitute the points into equation

  • For point, (35,118)

[tex]118=35^2A+35B+C[/tex]

[tex]118=1225A+35B+C[/tex] -------------(1)

  • For point, (45,218)

[tex]218=45^2A+45B+C[/tex]

[tex]218=2025A+45B+C[/tex] -------------(2)

  • For point, (55,563)

[tex]563=55^2A+55B+C[/tex]

[tex]563=3025A+55B+C[/tex] -------------(3)

Solve system of equation and find out A, B and C using calculator.

[tex]A=\dfrac{49}{40},B=-88,C=\dfrac{13579}{8}[/tex]

Quadratic model:

[tex]p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}[/tex]

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