If the exponential equation of best fit is y= 2.9046(1.9798)^x, when will the population be more than 13 million?
How would I figure this out?
I already determined the population in 30 days was 2,299,989,909 which is quite far from 13 million, but that gave me the number of days to figure out. How do I figure out when they give me the answer and I have to figure out the number of days?
y=2.9046(1.9798)^x
Solve for y=13. So:
13=2.9046(1.9798)^x
13/2.9046=1.9798^x
4.47566=1.9798^x
ln 4.47566=ln 1.9798^x=x ln 1.9798
x=2.1942355
The number of days, at that rate, would be 2.1942355
☺☺☺☺
except you want
2.9046(1.9798)^x = 13000000
x = 22.42
Thank you, but could you tell me how I would enter this into my calculator?
the same way you did it, but using the right value of 13,000,000 instead of 13.
To find out when the population will be more than 13 million, you need to solve the exponential equation for the value of x when y is greater than 13 million.
The exponential equation of best fit given is:
y = 2.9046 * (1.9798)^x
To solve for when the population will be more than 13 million:
1. Set the equation equal to 13 million:
13 million = 2.9046 * (1.9798)^x
2. Divide both sides of the equation by 2.9046:
(13 million / 2.9046) = (1.9798)^x
3. Take the logarithm (base 1.9798) of both sides of the equation to isolate x:
log(base 1.9798) [(13 million / 2.9046)] = x
4. Use a calculator to evaluate the logarithm. The value you obtain for x will represent the number of days when the population will be more than 13 million.
Note: It's important to ensure that the base of the logarithm matches the base of the exponential term. In this case, we log the equation with base 1.9798 (the base of the exponential term).
Please keep in mind that if the value you obtained for x is beyond the data range used to fit the exponential equation, it might not accurately predict the population. Additionally, if the equation was fitted based on limited data, its accuracy might decrease as you project further into the future.