Question

A town has population 225 people at year t=0. Write a formula for the population, P, in year t.

a) grows by 10% per year
I don't understand how to do this, and keep getting the wrong answer.

Also, Find a formula for the linear function q(x) whose graph intersects the graph of y=6000e−x/20 at x=20, x=120.

I have no clue to even attempt this. Thank you!

Answer 1

P = 225 * 1.1^t

Explanation: Every year, the population grows by 10%, so you multiply by 110% for the first year, 110%*110% for the second year, etc.

Evaluate y=6000e−x/20 at x = 20 and at x = 120

y(20)=6000e−20/20 = 6000 * e^-1 = 2207

y(120)=6000e−120/20 = 6000 * e^-6 = 14.87

So find a linear equation through the two points (20, 2207) and (120, 14.87)

which is of the form y = mx + b, where m is the slope, and b is the y intercept

The slope is (14.87-2207)/(120-20)
The y intercept is found by plugging one point into the equation and solving for b

2207 = ((14.87-2207)/(120-20))*20 + b

Solve for b and you have found your equation