Respuesta :
The domain of the exponential function that represents the situation if 1990 represents year 0 is all real numbers.
What is exponential function?
As the name implies, exponential functions make use of exponents. The base and exponent of an exponential function, however, are not a constant and a variable, respectively (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
For the given situation,
In year 1990, Jamaica's population, P₀ = 2,466,000
Rate of population growth, r = 1.1 % = 0.011
Let x be the number of years,
Then the growth of population can be written as:
[tex]P(x) = P_0 (1+r)^x[/tex]
Now, let's substitute the above values in this eqn,
[tex]P(x) = 2466000 (1+0.011)^x[/tex]
For x = 0,
[tex]P(0) = 2466000 (1+0.011)^0[/tex]
[tex]P(0) = 2466000[/tex]
For finding the population growth in future years, we need to use positive values of x.
For finding the population growth in past years, we need to use negative values of x.
For finding the intermediate values, then we need to use rational numbers.
Therefore, The domain of the exponential function is all real numbers.
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