Question

A species of plant experiences exponential growth after it is introduced into an area where it has never been. Which statement best describes exponential growth?

Answer 1

C. Within a few years the population increases dramatically

True. As we can see on the function
`A = A_o e^(rt)` if we increase the time by 10 units for example the final amount is increasing by a factor of
`e^(10)=22026.47` and that represent a dramatically increase.

Explanation:

When we have a exponential growth model the general formula is given by:

`A = A_o e^(rt)`

Since says "growth" the rate of increase r>0,
`A_o` represent the initial amount and A the amount after the time t.

Assuming the possible options for the answer. We analyze one by one

A. Each individual plant grows much larger than usual

False, for this model we assume that all the individuals in the population modeled have similar characteristics, because if the individuals are different we can't use a deterministic model like this one.

B. The population immediately decreases

False. We are assuming that the model is for a growth rate so then is not possible to have a decrease.

C. Within a few years the population increases dramatically

True. As we can see on the function
`A = A_o e^(rt)` if we increase the time by 10 units for example the final amount is increasing by a factor of
`e^(10)=22026.47` and that represent a dramatically increase.

D. The specie's reproductive potential declines

False, we are considering a growth model in which it makes no sense to consider that the potential, population or quantity measured decrease.