Ahypothetical metal alloy has a grain diameter of 2.4 × 10−2 mm. after a heat treatment at 575°c for 500 min, the grain diameter has increased to 4.1 × 10−2 mm. compute the time required for a specimen of this same material (i. e., d0 = 2.4 × 10−2 mm) to achieve a grain diameter of 5.5 × 10−2 mm while being heated at 575°c. assume the n grain diameter exponent has a value of 2.2.

50 inches should be the resultant vector

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.