In 1998, the population of a given country was 37 million, and the exponential growth rate was 5% per year. Find the exponential growth function
Population = 37*10^6 * (1.05)^t
where t is the number of years since 1998
To find the exponential growth function, we need to use the formula:
P(t) = P0 * e^(r * t)
Where:
- P(t) is the population at time t
- P0 is the initial population
- e is the base of the natural logarithm (approximately 2.71828)
- r is the growth rate as a decimal (percentage divided by 100)
- t is the time in years
In this case, the initial population (P0) is given as 37 million. The growth rate (r) is 5% per year, which can be expressed as 0.05. And the time (t) is not given, so we leave it as a variable.
Therefore, the exponential growth function for this scenario is:
P(t) = 37,000,000 * e^(0.05 * t)
Please note that this formula gives the population at any given time t. To calculate the population after a specific number of years, you need to substitute t with that value.