Answer:
The population will reach 20,400 after 6 years.
Step-by-step explanation:
Exponential function:
![y(t)=y_0(1+r)^t](https://tex.z-dn.net/?f=y%28t%29%3Dy_0%281%2Br%29%5Et)
y(t)= Population after t years
= initial population
r= rate of grow
t= time.
A town has a population of 17,000 and grows at a rate 3% every year.
y(t)= 20,400,
= 17,000, r=3%=0.03, t=?
![20,400=17,000(1+0.03)^t](https://tex.z-dn.net/?f=20%2C400%3D17%2C000%281%2B0.03%29%5Et)
![\Rightarrow \frac{20,400}{17,000}=(1.03)^t](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B20%2C400%7D%7B17%2C000%7D%3D%281.03%29%5Et)
![\Rightarrow \frac{102}{85}=(1.03)^t](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B102%7D%7B85%7D%3D%281.03%29%5Et)
Taking ln function both sides
![\Rightarrow ln|\frac{102}{85}|=ln|(1.03)^t|](https://tex.z-dn.net/?f=%5CRightarrow%20ln%7C%5Cfrac%7B102%7D%7B85%7D%7C%3Dln%7C%281.03%29%5Et%7C)
![\Rightarrow ln|\frac{102}{85}|=t\ ln|(1.03)|](https://tex.z-dn.net/?f=%5CRightarrow%20ln%7C%5Cfrac%7B102%7D%7B85%7D%7C%3Dt%5C%20ln%7C%281.03%29%7C)
![\Rightarrow t=\frac{ln|\frac{102}{85}|}{\ ln|(1.03)|}](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%5Cfrac%7Bln%7C%5Cfrac%7B102%7D%7B85%7D%7C%7D%7B%5C%20ln%7C%281.03%29%7C%7D)
⇒ t = 6 year.
The population will reach 20,400 after 6 years.
Assuming that the given rate is constant or that it can be used to in ratio and proportion solutions, we can use this to find the number of plates washed in any given amount of time. The formula would be:
17/10 = P/t
P = 17t/10
So, at just replace t in minutes to determine the number of plates washed, P.
Answer: Parallel lines have the same slope
y = 2x +b
Use the given point (2, 5)
5 = 2(2) +b
b = 5 -4 = 1
The equation of the line is
y = 2x +1
Note general form of the slope-intercept form of a line is y = mx +b, where m is the slope and b is the y-axis intercept
Step-by-step explanation:
Area formula for rectangles: L x W
Answer: 3 x 2a + 3 x 5 = 3 x 2a x 5
You know that the expressions are equivalent, because when you solve for a you get a = 5/8 or 0.625
Area: 12+30= 42
42/2=21
21 x 24=504
Area= 504
Perimeter = 12+30+24.7+26.8=93.5
Hope this helps :)