Write the first five terms of a geometric sequence in which the sixth term is 64.
1 answer:
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The exponential growth formular is given by
where: P is the population of the country, t years after the initial year (i.e. in this case, 1994).
is the initial population of the country (i.e. the population of the country in 1994).
r is the growth rate of the population and
t s the number of years after the initial year.
We obtain the value of r by comparing the growth between 1994 and 1998.
Here: P = 146,
, and t = 4 years
Thus
![146=140(r)^4 \\ \\ r^4= \frac{146}{140} =1.042857 \\ \\ r= \sqrt[4]{1.042857} =1.010546](https://tex.z-dn.net/?f=146%3D140%28r%29%5E4%20%5C%5C%20%20%5C%5C%20r%5E4%3D%20%5Cfrac%7B146%7D%7B140%7D%20%3D1.042857%20%5C%5C%20%20%5C%5C%20r%3D%20%5Csqrt%5B4%5D%7B1.042857%7D%20%3D1.010546)
To estimate the population of the country in 2011, we note that 2011 is 17 years after 1994.
Thus, the population of the country in 2011 can be estimated to be
million
Therefore, the population of the country in 2011 can be estimated to be 167 million to the nearest million.
where: P is the population of the country, t years after the initial year (i.e. in this case, 1994).
r is the growth rate of the population and
t s the number of years after the initial year.
We obtain the value of r by comparing the growth between 1994 and 1998.
Here: P = 146,
Thus
To estimate the population of the country in 2011, we note that 2011 is 17 years after 1994.
Thus, the population of the country in 2011 can be estimated to be
Therefore, the population of the country in 2011 can be estimated to be 167 million to the nearest million.