the population of a city of 750,000 people is devastated by an unknown virus that kills 20% of the population per day. how many people are left after a week? write the exponential equation to the situation.
15000
To find out how many people are left after a week, we need to calculate the population for each day and keep track of the remaining population.
The exponential equation for this situation can be represented by the formula: P = P0 * (1 - r)^t, where:
- P is the final population after t units of time.
- P0 is the initial population.
- r is the rate of decrease or mortality rate per day, expressed as a decimal.
- t is the number of days.
In this case, the initial population (P0) is 750,000, and the mortality rate (r) is 20% per day, which can be expressed as 0.2. We are interested in finding the final population after one week, which is equivalent to seven days (t = 7).
Plugging in these values into the exponential equation, we have:
P = 750,000 * (1 - 0.2)^7
Now we can calculate the result.