Answer:
<h3>2036</h3>
Step-by-step explanation:
Given the population of a city is modeled by the exponential function
ƒ (x) = 689,254 · 2.4e^0.014x, where x is the number of years after 2000
In order to determine the year that the city's population will exceed one million, we will substitute f(x) = 1,000,000 and find x first as shown:
1,000,000 = 689,254 2.4e^0.014x,
1000000/689,254 = 2.4e^0.014x,
1.4508 = 2.4e^0.014x,
1.4508 /2.4 = e^0.014x,
0.6045 = e^0.014x,
Apply ln to both sides
ln 0.6045 = lne^0.014x,
-0.5033 = 0.014x
x = -35.95
Since x cannot be negative, lets say x ≈ 36years
<em>This means that the population will exceed one million after about 36 years. The year it will exceed this amount will be 2000+36 = 2036</em>
<em>Note that the exponential equation used was not correctly written but the same calculation can be employed for any exponential functions you might have.</em>
