suppose that x and y vary inversely and x=1 when y=12. write a function that models the inverse variation. graph the function an
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ANSWER
EXPLANATION
We want to find the number of years that it will take the population to double.
To do this, we have to apply the exponential growth function:
where y = final value
a = initial value
r = rate of growth
t = time (in years)
For the population to double, it means that the final value must be 2 times the initial value:
Substitute the given values into the function above:
To solve further, convert the function from an exponential function to a logarithmic function as follows:
Solve for t:
It will take 9 years for the population to double.