A ceramic vase that cost an antique store $5 was marked $20. What is the percentage markup on the price of the ceramic vase?

Mathematics

1 answer:

Anika [276]3 years ago

8 0

The answer would be 75%%%%

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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

Natalija [7]

Answer:

It'll take approximately 34 years from today.

Step-by-step explanation:

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:

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