Question

The average lifespan of individuals in a population was measured before and after the cure for a disease was discovered. The average lifespan before the cure was discovered, b, gradually increased over several years to a, the average lifespan after the cure was discovered.

Which of the following functions would best model the situation above?

A.
exponential
B.
logarithmic
C.
step
D.
absolute value

Answer 1

A.

exponential

Explanation:

Exponential is best suited here because life span gradually increases from b to a over the years continuously. Whenever there is a continuous steady increase, exponential function is more suitable.

Logrithamic function will not suit because rate of change of log is 1/x and if x population is very large this will be almost equal to 0 which is not correct.

But exponential say a^x rate of increase= a^x log a and when a is small this will represent a slow steady state of increase.

Step function will not suit as step functions are discontinuous at every integral value, but the population function is a continuous function.

Absolute value function is suitable only for functions symmetrical about a particular value of x or y

But here there is no symmetry but steady increase. Hence exponential is the best suitable graph.