The Mexican long-tongued bat population is an endangered species, which decreases at a rate of 3.5% per year in a wildlife preserve that currently has 80 of them.
What type of function will model the population?
A)constant
B)exponential growth
C)linear decay
D)linear growth
E)exponential decay
Is it E)?
Well,
we know it can't be A, since it is changing
we know it can't be B, since it is not growing
not C or D, since it clearly is not linear.
is it exponential ? yes
Is it decay, is it getting less ? Yes
so .....
okay thank you
Yes, the correct answer is E) exponential decay.
To determine the type of function that will model the population, we can analyze the information given. The problem states that the Mexican long-tongued bat population is decreasing at a rate of 3.5% per year.
Exponential decay occurs when a quantity decreases at a constant percentage rate over time. In this case, the population is decreasing at a rate of 3.5% per year, which is a constant percentage rate. Therefore, an exponential decay function would be the most appropriate to model the population.
Exponential decay can be represented by the equation: P(t) = P₀ * e^(kt), where P(t) represents the population at time t, P₀ represents the initial population, e is Euler's number (approximately 2.71828), k is the decay constant, and t is time.
In this problem, the initial population (P₀) is given as 80 bats. Since the population is decreasing, the decay constant (k) would be negative. By plugging in the given information, we can determine the specific equation that models the population.
Therefore, the correct answer is E) exponential decay.