Question

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.

Answer 1

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)

Answer 2

Answer:

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

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:

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