What is a growth factor in a table in a exponential function table and how to solve this math

(a) The growth factor is 1.9.

(b) The population after 10 and 15 years are 18393 and 455434 respectively.

(c)

(d) In 17 years population exceed one million.

Step-by-step explanation:

Given table represents an exponential function.

The general form of an exponential function is

          .... (1)

where, a is initial value and b is growth factor.

Consider any two point from the given table. (0,30) and (1,57).

The value of a is 30.

Divide both sides by 30.

Substitute a=30 and b=1.9 in equation (1).

        .... (2)

(a)

Therefore the growth factor is 1.9.

(b)

Substitute x=10 in equation (2), to find the population after 10 years.

Therefore the population after 10 years is 18393.

Substitute x=15 in equation (2), to find the population after 15 years.

Therefore the population after 15 years is 455434.

(c)

The equation of elk population p for any year n after the elk were first counted is

(d)

We need to find the number of years after that the population exceed one million.

Let in t years the population exceed one million.

Divide both sides by 30.

Taking ln both sides.

Divide both sides by ln(1.9).

Therefore in 17 years population exceed one million.

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0