Question 129419
{{{P(t)=P[0]e^(-0.04t)}}}
{{{P(t)=(1000000)e^(-0.04t)}}}
a) At time t=1,
{{{P(1)=(1000000)e^(-0.04(1))}}} Substitute t=1.
{{{P(1)=(1000000)(0.960789)}}}
{{{P(1)=960789}}}
At 1 year, the population is now at 960,789.

b){{{P(t)=(1000000)e^(-0.04t)=750000}}}
{{{e^(-0.04t)=0.75}}}
{{{-0.04t=ln(0.75)}}} Take the natural log of both sides.
{{{-0.04t=-0.28768}}}
{{{t=7.19}}}
The time to reach 750,000 people would be 7.19 years (approximately 7 years, 2 months).
c){{{P(t)=(1000000)e^(-0.04t)=500000}}}
{{{-0.04t=ln(0.50)}}} Take the natural log of both sides. 
{{{-0.04t=-0.69315}}}
{{{t=17.33}}}
The time to reach 500,000 people would be 17.33 years (approximately 17 years, 4 months).