Mathematics: Population growth. port st. lucie, florida, had the united states fastest growth rate among cities with a population of 100,000 or more between 2003 and 2004. in 2003, the population was 103, 800 and increasing at a rate of 12% per year. in what year should the population reach 209,000 ? (let t = 0 correspond to 2003.) apply the formula n = n0 e^rt, where n represents the number of people. round your answer to one desimal place. t = .the tolerance is ±2%

She should choose 1 year and 8% ...

Population growth. port st. lucie, florida, had the

chaparro0512

12.01.2022

In 2009

Step-by-step explanation:

Since, the formula of population after t years,

$N=N_0 e^{rt}$

Where,

r = rate of growing per year,

Here, r = 12% = 0.12,

So, the population formula would be,

$N=N_0 e^{0.12t}$

If the population is estimated since 2003,

i.e. for 2003, t = 0,

We have N = 103, 800 for 2003,

$\implies 103800 = N_0 e^{0.12\times 0}=N_0 e^0 = N_0$

Thus, the function that shows the population after t years,

$N = 103800 e^{0.12t}$

If N = 209,000,

$209000 = 103800 e^{0.12t}$

$\frac{209000}{103800} = e^{0.12t}$

$2.01349 = e^{0.12t}$

Taking ln on both sides,

$\ln ( 2.01348 ) = 0.12t$

$\implies t = \frac{\ln(2.01348)}{0.12}=5.8\approx 6$

∵ 2003 + 6 = 2009

Hence, in 2009, the population should reach 209,000.

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