Question

the bear population increases at a rate of 2% each year there are 1573 bears this year, what is the growth factor b

Answer 1

The population will increase BY 2% each year.
It will increase TO 102% of its previous value each year.

102% is your growth factor,
as a decimal this is
`\rm b=1.02`

Hope that helps! :)

Answer 2

Using the formula:

`P = P_0(1+r)^t`

where

`P_0` is the initial population

r is the rate in decimal

b = 1+r is the growth factor

t is the time in years.

As per the statement:

the bear population increases at a rate of 2% each year there are 1573 bears this year,

⇒
`P_0 = 1573`, r = 2% = 0.02

then;

`P=1573(1+0.02)^t`

⇒
`b = 1+r= 1+0.02 = 1.02`

Therefore, the growth factor b is, 1.02