Exponential functions are functions defined by y = ab^x, where a represents the initial value, and b represents the rate
<h3>The equation of a city that has experienced a population growth</h3>The initial population of the city is 10000, and the growth rate of the population is 4%.
So, the exponential equation is:
The initial population of the city is 12000, and the decay rate of the population is 3%.
So, the exponential equation is:
The similarity in both equations is that, they both represent exponential function.
<h3>The year the population of city A exceeds B</h3>In (a) and (b), we have:
---- city A
--- city B
When city A exceeds city B, we have the following inequality
Divide both sides by 10000
Divide both sides by 0.97^x
Take the natural logarithm of both sides
This gives
Solve for x
This means that, the population of city A will exceed city B after 3 years
<h3>The year the population of city A will be at least twice of city B</h3>In (a) and (b), we have:
---- city A
--- city B
When city A is at least twice city B, we have the following inequality
Divide both sides by 10000
Divide both sides by 0.97^x
Take the natural logarithm of both sides
This gives
Solve for x
This means that, the population of city A will be at least twice city B after 13 years
Read more about exponential functions at: