The function [tex]y=0.3^x[/tex] represents exponential growth with the initial value equal to 1, the decay factor equal to 0.3, and the rate equal to 0.7.
Population Growth Equation
The formula for the Population Growth Equation is:
[tex]P_f=P_o*(1+\frac{R}{100}) ^t[/tex]
Pf= future population
Po=initial population
r=growth rate
t= time (years)
growth or decay factor = (1 ±r)
When 1+R > 1, the equation represents growth, while 1+R < 1 the equation represents decay.
The question gives:
[tex]y=0.3^x[/tex], then
Pf=y
Po= 1
[tex](1+\frac{R}{100}) =0.3[/tex] , thus
[tex](100+R}) =30\\ \\ R=-100+30\\ \\ R=-70[/tex]
r= -70%= -0.7
decay factor= (1-0.7)=0.3
Therefore,
1+R will be = 1+(-0.7)=1 - 0.7 =0.3
When 1+R >1, the function represents exponential growth.
Read more about the exponential function here:
brainly.com/question/8935549
