Which equation represents a population of 210 animals that decreases at an annual rate of 14%?

A. [tex] P(t) = 210(0.86)^t [/tex]
B. [tex] P(t) = 210(1.14)^t [/tex]
C. [tex] P(t) = 210(0.14)^t [/tex]
D. [tex] P(t) = 210 - 14t [/tex]

(Note: Ensure to choose the option that correctly represents an exponential decay equation.)

Question

College

Answer :

CrimsonBlow CrimsonBlow · Answer 1 · 2024-03-09T17:11:26-05:00

Answer:

The equation i.e. used to denote the population after x years is:

P(x) = 490(1 + 0.200 to the power of x

Step-by-step explanation:

This problem could be modeled with the help of a exponential function.

The exponential function is given by:

P(x) = ab to the power of x

where a is the initial value.

and b=1+r where r is the rate of increase or decrease.

Here the initial population of the animals are given by: 490

i.e. a=490

Also, the rate of increase is: 20%

i.e. r=20%

i.e. r=0.20

Hence, the population function i.e. the population of the animals after x years is:

P(x) = 490(1 + 0.200 to the power of x

dennistorresjr0801 dennistorresjr0801 · Answer 2 · 2024-12-11T06:29:26-05:00

So for this, we will be using exponential form, which is y = ab^x (a = initial value, b = growth/decay).

Since we start off with 210 animals, that is our a variable.

Next, since this is *decreasing* by 14%, you are to subtract 0.14 (14% in decimal form) from 1 to get 0.86. That will be your b variable.

Putting everything together, your equation is y = 210(0.86)^x