Application of the Exponential and Logarithm:
a) The population size of a country declines exponentially at a rate of 2.1% per year. If the population was 35.7 million in the year 2012, then what is the population size in the year 2017?

b) The number of ants in an colony increases exponentially at a rate of 4.6% per week. How long do you have to wait until the ant colony has tripled in size?

Question

Application of the Exponential and Logarithm:
a) The population size of a country declines exponentially at a rate of 2.1% per year. If the population was 35.7 million in the year 2012, then what is the population size in the year 2017? 

b) The number of ants in an colony increases exponentially at a rate of 4.6% per week. How long do you have to wait until the ant colony has tripled in size?

anonymous · Answer

to decrease a number by $2.1\%$ multiply it by $100\%-2.1\%=97.8\%=.978$

anonymous · Answer

since 2017 is 5 years after 2012 your answer will be 
$$35.7\times (.979)^5$$

anonymous · Answer

ooh typo there
100-2.1=97.9
answer is correct though

anonymous · Answer

ahh XD .978 thanks man im terrible with word problems

anonymous · Answer

@satellite73 is the same done for question b?

anonymous · Answer

@satellite73 you there bro