Every year a lake becomes more polluted, and 5% fewer organisms can live in it. If in 2010 there are one million organisms, write an equation relating N, the number of organisms (in millions), to time t, in years since 2010.
N = 1E6 (1 - .05)^t
We can write the equation as follows:
N = (1 - 0.05)^t
Where:
N = number of organisms in millions
t = time in years since 2010
In this equation, (1 - 0.05) represents the percentage of organisms that can survive each year, and t represents the number of years that have passed since 2010.
To write an equation relating the number of organisms to time, we need to consider the decrease in organisms over time.
First, let's define some variables:
- N: the number of organisms (in millions)
- t: time in years since 2010
Given that every year the lake becomes more polluted and 5% fewer organisms can live in it, we can determine the relationship between the number of organisms and time.
Starting with one million organisms in 2010, we can express this as the starting value for N, which is N0 = 1 million.
Now, let's consider the decrease in organisms each year. Each year, there will be 5% fewer organisms than the previous year. This means that the number of organisms will be decreasing by 5% each year.
To represent a decrease of 5% each year, we can express it as a multiplier of 0.95 (1 - 0.05) each year.
Therefore, we can write the equation relating N to t as follows:
N(t) = N0 * (0.95)^t
Since N0 is given as 1 million (or 1 in terms of millions), the equation becomes:
N(t) = 1 * (0.95)^t
So, the equation relating the number of organisms (N) to time (t) is N(t) = (0.95)^t, where t is the time in years since 2010.