The inverse of the function is k(x) =
You can find the inverse of any function by switching the k(x) value and the x value. After that, solve for the new k(x). The result will be your inverse function. The step-by-step process is below.
k(x) = 10x + 5 ----> Switch the x and k(x)
x = 10k(x) + 5 ----> Subtract 5 from both sides
x - 5 = 10k(x) ----> Divide both sides by 10.
= k(x) ----> Now switch the order for formatting
k(x) =
And this is your new inverse function.
Answer:
624 people
(I put two ways to look at the problem.)
Step-by-step explanation:
What is describe here is an exponential function of the form:
is the number of years after 1761.
is the initial population.
So t=0 represents year 1761.
t=1 represents year 1762
t=2 represents year 1763
....
t=20 represents year 1781.
So we have the doubling time is 5 years. This means the population will be twice what it was in 5 years. Let's plug this into:
Divide both sides by :
Convert to logarithm form:
Multiply both sides by 1/5:
By power rule.
So in the next sentence they actually give us the initial population and we just found k so this is our function for P:
So now we plug in 20 to find how many residents there were in 1761:
This is surely going to the calculator:
Now if you don't like that, let's try this:
Year 0 we have 39 people.
Year 5 we have 39(2)=78 people.
Year 10 we have 78(2)=156 people.
Year 15 we have 156(2)=312 people.
Year 20 we have 312(2)=624 people.