Mathematics: 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.

sureStep-by-step explanation:...

An insurance company charges a 35-year old non-smoker

keigleyhannah30

17.01.2022

$p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}$

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)

118=35^2A+35B+C

118=1225A+35B+C -------------(1)

For point, (45,218)

218=45^2A+45B+C

218=2025A+45B+C -------------(2)

For point, (55,563)

563=55^2A+55B+C

563=3025A+55B+C -------------(3)

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

$A=\dfrac{49}{40},B=-88,C=\dfrac{13579}{8}$

Quadratic model:

$p=\dfrac{49}{40}a^2-88a+\dfrac{13579}{8}$

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