The function P(t)=87,000e^0.106t models the population of a city, t years after 2010. How many people lived in the city in 2010? At what rate is the population change in? Explain

87,000 ; 10.6%

Step-by-step explanation:

Given the function :

P(t)=87,000e^0.106t

P(t) is an exponential function ; comparing the given function to the general form of an exponential function :

y = Ae^rt

Where,

A = initial amount ; r = growth rate ; t = time

The Given function models t years after 2010, that is the 2010 population is the initial population of the city.

Comparing the general exponential equation with the function given:

A = 87,000 = population of city in 2010

The growth rate :

rt from the general equation compares to 0.106t in the given function.

rt = 0.106t

r = 0.106

Hence, the rate of change = 0.106 * 100% = 10.6%

Alright, the angles ∠A and ∠B  are corresponding angles meaning they have the same degree value!

∠A = 8x - 8°

∠B = 5x + 25°

To find ∠B, however, we're going to need to know the value of x !

The only way we're going to find what x is, is to set the angles equal to each other ...

Do as follows:

∠A = ∠B

8x - 8 = 5x + 25

Combine like terms

8x = 5x + 25 + 8

8x = 5x + 33

8x - 5x = 33

3x = 33

x = 11

Now plug in x to find the value of ∠B

∠B = 5(11) + 25°

∠B = 55 + 25°

∠B = 80°