SOLUTION: In 2004 the population of the US was 294.4 million. If the population grows at a rate of 1.05% then the population in the year 2015 will be 294.4million(1.0105) to the 11th power

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Question 55020: In 2004 the population of the US was 294.4 million. If the population grows at a rate of 1.05%
then the population in the year 2015 will be 294.4million(1.0105) to the 11th power.
A) Evaluate the expression to find the predictrd population in 2015 to the nearest tenth of a million people.

B) Which year will the population will reach 350 million people.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can generalise the population growth formula to predict the population n years after 2004 by:
P+=+294.4X10%5E6%281.0105%29%5En
A) The predicted population in 2015 (11 years after 2004) is:
P+=+294.4X10%5E6%281.0105%29%5E11
P+=+330.246X10%5E6 Round to the nearest tenth of a million.
P+=+330.2Million.
B) The year in which the predicted population will be 350 million can be found by using the formula derived above and solving for n. Remember that n is the number of years after 2004.
P+=+294.4X10%5E6%281.0105%29%5En Set P+=+350X10%5E6 and solve for n.
350X10%5E6+=+294.4X10%5E6%281.0105%29%5En Divide both sides by 294.4X10%5E6
%28350X10%5E6%29%2F%28294.4X10%5E6%29+=+%281.0105%29%5En Simplify.
1.18886+=+%281.0105%29%5En Take the logarithm of both sides.
log%28%281.18886%29%29+=+nlog%281.0105%29 Divide both sides by log%28%281.0105%29%29
n+=+%28log%28%281.18886%29%29%29%2F%28log%28%281.0105%29%29%29 Use your calculator to evaluate this.
n+=+16.54
Round to 17 and add to 2004
2004 + 17 = 20021
The population should reach 350 million in the year 2021