-
If the population continues to decline at this rate, to what fraction of the original population size will the population decline after 10 years?
(Keep at least 4 significant digits.)
Hint
If the population is decreasing at a rate of 5% per year, then by what number do we need to multiply the population size each year?
Hide help
-
To what fraction of the original population size will the population decline after $n$ years?
(Online, enter exponentiation using ^, so enter $a^b$ as a^b.)
Hint
Same procedure as for the previous part, except that you have multiply by that number $n$ times.
Hide help
-
To find how long it will take for the population to decline by one-half, follow these steps. Set the expression from part (b) equal to one-half.
$ = \frac{1}{2}$
Take the logarithm of both sides of that equation.
=
(Online, you can use either ln or log for logarithm; both are interpreted a logarithm base $e$. In this case, it doesn't matter what base logarithm you use.)
Using the log of power rule, bring down the exponent from the left hand side in front of the logarithm.
=
Solve for the value of $n$. The result is a ratio of logarithms.
$n=$
$\approx$
(In the first blank, write the ratio of logarithms. In the second blank, give a decimal approximation with at least 4 significant digits.)
To repeat, how many years will it take for the population to decline by one-half?
(The second blank is for a unit.)
-
You can use a similar procedure to find out how long it will take for the population to decline to one-tenth its original size. Set the expression from part (b) equal to one-tenth.
$ = \frac{1}{10}$
Take the logarithm of both sides of that equation.
=
(Online, you can use either ln or log for logarithm; both are interpreted a logarithm base $e$. In this case, it doesn't matter what base logarithm you use.)
Using the log of power rule, bring down the exponent from the left hand side in front of the logarithm.
=
Solve for the value of $n$. The result is a ratio of logarithms.
$n=$
$\approx$
(In the first blank, write the ratio of logarithms. In the second blank, give a decimal approximation with at least 4 significant digits.)
To repeat, how many years will it take for the population to decline to one-tenth of its original size?
(The second blank is for a unit.)
-
If the current population size is 100,000, how long will it take for the population drop down to 5,000 sea lions?
(Keep at least 4 significant digits. Second blank is for a unit.)
Hint
To get to 5,000 sea lions, you need to get down to what fraction of the original population? The rest is the same as the previous problems.
Hide help