Use the formula t=ln2/k that gives the time for a population, with a growth rate k, to double, to answer the following question.
the growth modes a=8e^0.005t describes the population, a, of a country in millions, t years after 2003.
what is the countries growth rate? how long will it take the country to double its population?

a)

We have that the countries growth rate k is given below as

,

b)

And it will take the country to double its population.

a)

From the question we are told that:

Formula time for a population growth rate double

Growth modes

With as the Growth factor

Therefore

Natural Logarithm

b)

Generally, the equation for time t is mathematically given by

Therefore

In conclusion

Is the countries growth rate k is given below as

And with the growth rate we derived How long will it take the country to double its population as

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Step-by-step explanation:

Matching the form

  A = A0·e^(kt)

to the given equation

  A = 8·e^(.005t)

we can identify the value of k as being 0.005.

  k = 0.005

___

The doubling time is given by the formula ...

  t = ln(2)/k = ln(2)/0.005 ≈ 138.63

It will take about 139 years for the population to double.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

2/3x + 7 = 29

step-by-step explanation:

two thirds = 2/3

plus a number = x

at least 29 = 29

there for you should get 2/3x + 7 = 29