Question

In 2004 the population in Morganton, Georgia, was 43,000. The population in Morganton doubled by 2010. If the growth rate remains the same, what is the expected population in Morganton in 2020?

Answer 1

Answer:

263,606.9

Step-by-step explanation:

In 2004 the population in Morganton, Georgia, was 43,000.

(0, 43000)

The population in Morganton doubled by 2010

In 6 years the population is doubled (86000)

(6,86000)

$A= a(b)^t$

Use (0,43000) in the above equation

$A= a(b)^t\\43000= a(b)^0\\a=43000$

Now plug in (6,86000)

$A= a(b)^t\\A= 43000(b)^t\\86000=43000(b)^6\\2=b^6\\b=\sqrt[6]{2} \\b=1.12$

$A=43000(1.12)^t$

Now find out A when t=16 (2020)

$A=43000(1.12)^t\\A=43000(1.12)^{16}\\A=263606.9$