3 years ago

What two forms can you write 4.293

Mathematics

1 answer:

Lerok [7]3 years ago

8 0

4.293

=4+(293/1000)

=(4000/1000)+(293/1000)

=4293/1000

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A bird species in danger of extinction has a population that is decreasing exponentially (A = A0e^kt). Five years ago, the popul

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It'll take approximately 34 years from today.

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in order to solve this problem we first need to find the rate of change, "k", to do that we will use the given information where the population was 1400 five years ago and its now 1000. Applying this data to the equation gives us:

$A = A_0*e^{k*t}\\1000 = 1400*e^{5*k}\\1400*e^{5*k} = 1000\\e^{5*k} = \frac{1000}{1400}\\ln(e^{5*k}) = ln(\frac{1000}{1400})\\5*k = ln(1000) - ln(1400) \\k = \frac{ln(1000) - ln(1400)}{5} = -0.06729$

We now know the value for "k", we can estimate how many years it will take for the bird population to dip below 100. We have:

$100 = 1000*e^{-0.06729*t}\\e^{-0.06729*t} = \frac{100}{1000}\\ln(e^{-0.06729*t} = \frac{1}{10}\\-0.06729*t = ln(0.1)\\t = -\frac{ln(0.1)}{0.06729} = 34.22$

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4 years ago