In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C and a so that P(x)equalsCa Superscript x minus 2000 models the population of a country in year x. (b) Estimate the country's population in 2010. (c) Use P to determine the year when the country's population might reach 1.4 billion. (a) Cequals nothing (Type an integer or decimal rounded to five decimal places as needed.)

(a) The value of C is 1.

(b) In 2010, the population would be 1.07555 billions.

(c) In 2047, the population would be 1.4 billions.

Step-by-step explanation:

(a) Here, the given function that shows the population(in billions) of the country in year x,

So, the population in 2000,

According to the question,

(b) Similarly,

The population in 2025,

                   (∵ C = 1)

Again according to the question,

Taking ln both sides,

Thus, the function that shows the population in year x,

    ...... (1)

The population in 2010,

Hence, the population in 2010 would be 1.07555 billions.

(c) If population P(x) = 1.4 billion,

Then, from equation (1),

Therefore, the country's population might reach 1.4 billion in 2047.