Answer:
The year is 2020.
Step-by-step explanation:
Let the number of years passed since 2010 to reach population more than 7000000 be 'x'.
Given:
Initial population is, [tex]P_0=450,000[/tex]
Growth rate is, [tex]r=5\%=0.05[/tex]
Final population is, [tex]P=700,000[/tex]
A population growth is an exponential growth and is modeled by the following function:
[tex]P=P_0(1+r)^x[/tex]
Taking log on both sides, we get:
[tex]\log(P)=\log(P_0(1+r)^x)\\\log P=\log P_0+x\log (1+r)\\x\log (1+r)=\log P-\log P_0\\x\log(1+r)=\log(\frac{P}{P_0})\\x=\frac{\log(\frac{P}{P_0})}{\log(1+r)}[/tex]
Plug in all the given values and solve for 'x'.
[tex]x=\frac{\log(\frac{700,000}{450,000})}{\log(1+0.05)}\\x=\frac{0.192}{0.021}=9.13\approx 10[/tex]
So, for [tex]x > 9.13[/tex], the population is over 700,000. Therefore, from the tenth year after 2010, the population will be over 700,000.
Therefore, the tenth year after 2010 is 2020.
