I posted this question yesterday that you answered, so thank you, but how do I put this in my calculator to get this answer?
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?
math - unowen yesterday at 2:53pm
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
☺☺☺☺
math - Steve yesterday at 4:17pm
except you want
2.9046(1.9798)^x = 13000000
x = 22.42
Steve may not be online right now.
Going with his equation,
2.9046(1.9798)^x = 13000000
first divide both sides by 2.9046
1.9798^x = 4475659.299.. (keep in your display)
take log of both sides, and use your log rules
x log 1.9798 = log 4475659.299
x = log 4475659.299/log 1.9798
= 22.42.. as Steve had
by keeping the 4475659.299.. in the display, we can just continue our sequence of calculations.
I then pressed:
log
=
/
log 1.9798
=
to get the answer
To figure out when the population will be more than 13 million using the given exponential equation of best fit, follow these steps:
1. Start with the exponential equation: y = 2.9046(1.9798)^x, where y represents the population and x represents the number of days.
2. Set up the equation by equating y to 13 million: 2.9046(1.9798)^x = 13000000.
3. Divide both sides of the equation by 2.9046: (1.9798)^x = 13000000/2.9046.
4. Simplify the right side to obtain an approximate value: (1.9798)^x ≈ 4475.66.
5. Take the natural logarithm (ln) of both sides of the equation: ln[(1.9798)^x] = ln(4475.66).
6. Apply the logarithm rule to bring down the exponent: x ln(1.9798) = ln(4475.66).
7. Divide both sides of the equation by ln(1.9798): x = ln(4475.66) / ln(1.9798).
8. Use a calculator to find the values of ln(4475.66) and ln(1.9798), then divide them to get the value of x. In this case, x ≈ 22.42.
Therefore, the number of days it will take for the population to exceed 13 million is approximately 22.42 days.