Answer:
1 year
Step-by-step explanation:
The population can be modelled by the equation:
[tex]P=P_0(1 + r)^{t} [/tex]
From the question, the initial population is
[tex]P_0=19000[/tex]
The annual growth rate is r=0.04
We want to find how long it will take for that population to reach 43500.
We substitute the values to get:
[tex]43500=19000(1 + 0.04)^{t} [/tex]
[tex]435=190(1.04)^{t} [/tex]
[tex] \frac{435}{190} = (1.04)^{t} [/tex]
[tex]t = \frac{ \ln(2.289) }{1.04} [/tex]
[tex]t = 0.7965[/tex]
To the nearest year, t= year
