Exponential growth rate for undefined values

[jlmango]

It is predicted that the population of a particular state will double by the year 2026. Determine the annual, monthly, and continuous growth rates.


I know that for this problem I am supposed to use f(x)=n₀e^rt I just have no idea where to start.

This one is throwing me off in particular because I have no value for n₀I only have an end date. 2026. Should I find the difference in years from now until 2026 and use that as my t value? and then my value for r would be 2 as the population grows by 200% at the end of the 14 years???
Thanks in advance for your helpfulnessessess

 

[jlmango]

Also having trouble with this

I am also having trouble with this problem I have attached my work to show my valiant attempt.

The number of people who hear a rumor tends to follow a saturated growth model. suppose a particular town has 2000 people. three days after a rumor is introduced, 140 people will have heard it. Determine when 40% of the population will have heard the rumor.

 

[HallsofIvy]

It is predicted that the population of a particular state will double by the year 2026. Determine the annual, monthly, and continuous growth rates.


I know that for this problem I am supposed to use f(x)=n₀e^rt I just have no idea where to start.

This one is throwing me off in particular because I have no value for n₀I only have an end date. 2026. Should I find the difference in years from now until 2026 and use that as my t value? and then my value for r would be 2 as the population grows by 200% at the end of the 14 years???
Thanks in advance for your helpfulnessessess

You don't need an initial quantity- just assume that is some value N in 2013 and 2N in 2026, 13 years.

 

[HallsofIvy]

I am also having trouble with this problem I have attached my work to show my valiant attempt.

The number of people who hear a rumor tends to follow a saturated growth model. suppose a particular town has 2000 people. three days after a rumor is introduced, 140 people will have heard it. Determine when 40% of the population will have heard the rumor.
View attachment 1596

It's very difficult to read that since the background is so dark- and part appears to have been cut off. If this problem is at all important to you, take the time to actually type it in:]
f(x)= a/(1- e^{kx})
The town has a population of 2000 and you have set a= 2000. Is "x" the time in days? That doesn't make sense to me. When x is 0, the denominator will be 0 and f(0) does not exist. If k is positive, f(x) will be negative for positive x and if k is negative, f(x) is a decreasing function.