Since January 1, 1960, the population of Slim Chance has been described by the formula P=30000(0.97)t, where P is the population of the city t years after the start of 1960. At what rate was the population changing on January 1, 1995?
The rate of change of the population on January 1, 1995 can be calculated by taking the derivative of the population formula with respect to time. This gives us the rate of change of the population as -290,000(0.97)t-1. On January 1, 1995, t = 35, so the rate of change of the population on that date is -290,000(0.97)35-1 = -8,845.
AAAaannndd the bot gets it wrong yet again!
It can't tell exponentials from polynomials
P = 30000(0.97)^t
P' = 30000 ln0.97 (0.97)^t
so P'(35) = -314.667