A city starts with a population of 500,000 people in 2007. Its population declines according to the equation P(t) = 500,000e -0.099
where P is the population in t years later. Approximately when will the population be one-half the initial amount?

A city starts with a population of 500,000 people in 2007. Its population declines according to the equation

P(t) = 500,000e -0.099t

where P is the population in t years later. Approximately when will the population be half the initial amount?

2014

Step-by-step explanation:

Given the exponential growth function :

P(t) = 500,000e^-0.099t

Where P is population in t years later

When the population will 1/2 the initial amount

1/2 the initial amount = 1/2 * 500,000 = 250,000

P(t) = 250,000

250,000 = 500000e^-0.099t

250,000/500000 = e^-0.099t

In(0.5) = - 0.099t

t = −0.69314 / - 0.099

t = 7.0014

t = 7

Year which population = 500,000 = 2007

Hence, half the population will be attained on (2007 + 7) = 2014