Question

A flock of 200 birds were flying south for the winter. Every day, the amount of birds in the flock increased by an average of 4%.

The amount of birds in the flock, b, can be represented by an exponential function, where d represents the number of days since the 200 birds started. What is the equation of this exponential function?
b = 1.04 · 200d

Answer 1

`b=200(1.04)^(d)`

Explanation:

we know that

The exponential function is of the form

`y=a(b)^(x)`

where

a is the initial value

b is the base

In this problem we have

a=200 birds

b=100%+4%=104%=104/100=1.04

substitute

`y=200(1.04)^(x)`

Let change of variables

`b=200(1.04)^(d)`

where

b is the amount of birds in the flock

d is the number of days since the 200 birds started