The half-life of the adioactive element Krypton-91 is 10 seconds. If 16 grams of Krypton-91 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50 seconds?

Use the exponential growth model A = A0e^(kt) to show that the time it takes a population to double (to grow fom A0 to 2A0) is given by t = (ln 2)/k

The growth model A = 4.1e^(0.01t) descibes New Zealand's population A, in millions, t years after 2006.
a) What is New Zealand's growth rate?
b) How long will it take New Zealand to double its population?

[Please refer to the attachment fo the rest of the problems]

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Logarithm and provides students with a clear perspective of the underlying concepts.

... scientists could find the product of two numbers m and n by looking up each number's logarithm in a special table, adding the logarithms together, and then ...

... To solve 7 x = 30, we can take the logarithm of each side of the equation to get log (7 x ) = log (30). The power rule for logarithms would then provide a way ...

... of above Question 1 to one based upon common logarithms rather than natural logarithms. ... The hint suggests the method to convert the logarithm of a number given ...

... is an example of how logarithms and exponents "cancel out". When you have a number raised to an exponent (23 for example), and you take the logarithm with the ...

... 2. Solve algebraically; 3. Write in terms of logarithms of x, y and z. 4. Rewrite as a single logarithm: 5. The population of a town is modeled by the equation ...

... 14. Write the expression as a sum and/or a difference of logarithms with all variables to the first degree. ... 17. Use a calculator to evaluate the logarithm. ...

... f(x)=2-x-4 6. Find the exact value of the logarithm without using a calculator. Log 1/232 7. Write the expression as a sum and/ or difference of logarithms. ...

... find each logarithm without using a calculator. 2. log10 (20/27). Please find solution/explanation attached. This solution uses the properties of logarithms to ...

... 6. Evaluate the following logarithms a. log216 b. log88 c.log3(1/27). ... detailed explanation how to solve questions related to exponent, power and logarithm. ...