00:01
In the given question we are told that the population of a town, the population of a certain country in 1995 was $290995 was $286 million.
00:20
The population of this country was $286 million in 1995 and we are told.
00:31
That in addition the population of the country was growing at a rate of 1 .1 percentage per year.
00:38
So growing at a rate of at a rate of 1 .1 percentage per year.
00:51
And now assuming that this growth rate continues, we are told that we can use a model given as p of t equals p of t equals 286 times 1 .011 raised to the power t minus 9095 so this is the model in which we are told that p of t represents the population in millions the population in millions in millions in the year t and what we are asked is when will the population of the country reach each of the following values and the first value the first number that is given to us is 340 million.
02:02
So to calculate in which year we would reach this number, we can just substitute for p of t as 340.
02:12
Then we would have the rest of the equation like this.
02:17
And from this we can write 340 divided by 286 is 1 .1 ,1 .188888.
02:30
And this is equal to 1 .011 raised to the power of t minus 1995.
02:38
In the next step we are going to use a logarithmic property after taking logarithm on both sides of this equation we can write log of 1 .011 raised to t minus 1995 we can use a property that says log of a to the power of b can be written as b times log of a so then we can write log of 1 .888 is equal to 0 .075113 and this is equal to according to this property we can write t minus 1995 times the log of 1 .011.
03:33
When we take the log of 1 .011, we get an answer.
03:39
Let's write over here, t minus 1995 as then equal to 0 .075113 divided by log of 1 .011 .1...