Why there will be a change in the sole of the shoes after using many days?

See the explanation below

Explanation:

Due to the frictional force, this force acts in the opposite direction to the movement of the person's shoe. This force tends to wear the sole of any shoe. We must remember that the frictional force is defined as the product of the normal force by the coefficient of friction between surfaces.

For this case, it should be the coefficient of dynamic friction between the pavement and the material of the sole of the shoe

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.