How to solve function with exponents

Question

The function f(x)=570(1.032)^x-1976 Models a populations, in millions, of an Asian country. 

 

a) Is it a growth or decay function 

b) What was the population in 2002?

c) When will the countries population be greater than 2.4 Billion

d) When did the countries population triple, according to this data?

 

The more information about to how to solve the better as I will be trying to figure out exactly how to do it. Thanks!

Answer 1

f(x)=570(1.032)^x-1976

 

a)  It's a growth function as long as x>1976

 

b)  f(2002) = 570(1.032)^2002-1976 = 570(1.032)²⁶

 

c)  2400 = 570(1.032)^x-1976

 

2400/570 = (1.032)^x-1976

 

ln(2400/570) = (x-1976)ln(1.032)                             [ln(a^b) = b ln(a)]

 

ln(2400/570)/ln(1.032) + 1976 = x

 

d)  Initial population is 570 million (in 1976).  Use solution from c) but use 570*3 vice 2400

 

ln(570*3/570)/ln(1.032) + 1976 = x

 

ln(3)/ln(1.032) + 1976 = x