Question

Solve each continous exponential growth/decay

17) For a period of time, an island's
population grows exponentially. If the
continuous growth rate is 3% per year and
the current population is 1,891, what will
the population be 5 years from now?

show work please

Answer 1

2198

Explanation:

Exponential growth problem.

P(t) = PO* e^(rt)

where:

PO = initial population

P(t) = population after time t

r = continuous growth rate

t = time

In this problem, we have:

PO= 1,891 (current population) r = 0.03 (3% per year as a decimal)

We want to find the population 5 years from now, so we can set t = 5:

P(5) = 1,891 * e^(0.03 * 5)

P(5) = 1,891 * e^0.15

P(5) = 1,891*1.1628

P(5) = 2,198.93

Therefore, the population 5 years from

now will be approximately 2,198 people.

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