Question

The population of osaka japan declined at an average annual rate of 0.05% for five years between 1995 and 2000. If the population of osaka was 11,013,000 in 2000 and it continues to decline at the same rate, predict the population in 2050

Answer 1

Answer:

$10,741,021\ people$

Step-by-step explanation:

we know that

The equation of a exponential decay function can be written as

$y=a(1-r)^x$

where

y ---> is the population of Osaka japan

x ---> the number of years since 2000

a ---> is the initial value or y-intercept

r is the rate of change

we have

$a=11,013,000\ people$

$r=0.05\%=0.05/100=0.0005$

substitute

$y=11,013,000(1-0.0005)^x$

$y=11,013,000(0.9995)^x$

Predict the population in 2050

so

$2050-2000=50\ years$

For x=50 years

substitute in the equation

$y=11,013,000(0.9995)^{50}$

$y=10,741,021\ people$