The population in certain country is growing at the rate of 7 % a year . If the population in the year 1995 was 190 million, (a)determine an exponential expression representing the population as a function of the year. (b) What will the population be in 2005 ? (c) What was the population in the 1999?

if t is the number of years since 1995, and p(t) is in millions, then

p(t) = 190*1.07^t

(a) To determine an exponential expression representing the population as a function of the year, we need to use the formula for exponential growth:

P(t) = P0 * (1 + r)^t

where:
P(t) is the population at time t
P0 is the initial population
r is the growth rate as a decimal
t is the time elapsed

Given that the population in 1995 (t=0) was 190 million, and the growth rate is 7% or 0.07, the exponential expression representing the population as a function of the year is:

P(t) = 190 * (1 + 0.07)^t

(b) To find the population in 2005, we substitute t = 10 into the equation:

P(10) = 190 * (1 + 0.07)^10
P(10) = 190 * 1.07^10
P(10) ≈ 190 * 1.96715
P(10) ≈ 374.9565 million

Therefore, the population in 2005 will be approximately 375 million.

(c) To determine the population in 1999, we substitute t = 4 into the equation:

P(4) = 190 * (1 + 0.07)^4
P(4) = 190 * 1.31225
P(4) ≈ 249.128 million

Therefore, the population in 1999 was approximately 249 million.