Respuesta :
A population with 14,000 organisms initially and grows by 18.7% each year can be represented in a exponential model given below:
[tex]p=p_{0} (b)^{\frac{t}{c}}=14000(0.187)^{t}[/tex]
Exponential function is a relation of the form [tex]y=a^{x}[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a. It is useful in modeling many physical phenomena, such as populations, interest rates, radioactive decay, and the amount of medicine in the bloodstream. An exponential model is of the form:
[tex]A=A_{0}( b)^{\frac{t}{c} }[/tex]
where
[tex]A_{0}[/tex] = the initial amount of whatever is being modelled.
t = elapsed time.
A = the amount at time, t.
b = the growth factor. Note that if b > 1, then we have exponential growth, and if 0< b < 1, then we have exponential decay.
c = time it takes for the growth factor b to occur.
Suppose p represents population, and t is the number of years of growth, the exponential model for the population written in the form p:
[tex]p=p_{0} (b)^{\frac{t}{c}[/tex]
[tex]p=14000(0.187)^{t[/tex]
where
p = the population at time t
[tex]p_{0}[/tex] = initial population of 14,000
b = growth factor of 18.7%
t = elapsed time (in years)
c = 1 as the growth occurs each year
To learn more about exponential functions: https://brainly.com/question/2456547
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