Respuesta :
Answer:
The forest A is growing at a faster rate as it has a larger base (1.029).
Step-by-step explanation:
We have been given that for each year t, the population of a forest of trees is represented by the function [tex]A(t)=113(1.029)^t[/tex]. In a neighboring forest, the population of the same type of tree is represented by the function [tex]B(t)=81(1.025)^t[/tex].
We know that an exponential growth function is in form [tex]y=a\cdot b^x[/tex], where,
y = Final value,
a = Initial value,
b = For growth base b is in form [tex](1+r)[/tex], where r represents rate in decimal form,
x = Time.
We know that the larger the base of an exponential function would be, the larger will be growth rate.
Upon looking at both functions, we can see that base of function [tex]A(t)=113(1.029)^t[/tex] is 1.029 and base of function[tex]B(t)=81(1.025)^t[/tex] is 1.025.
Since 1.029 is greater than 1.025, therefore, the forest population represented by function [tex]A(t)=113(1.029)^t[/tex] grows at a faster rate.
