Answer:
≈ 18.8 cm
Step-by-step explanation:
The arc length is calculated as
arc = circumference of circle × fraction of circle
The central angle is equal to the arc subtending it, that is 60°
arc = 2πr × 
= 2π × 18 × 
= 36π ×
= 6π ≈ 18.8 cm ( to 1 dec. place )
The equation for exponential decay is given as y = a(1 - r)^x.
<u>Explanation:</u>
The formula for original exponential decay is y = ab^x.
The growth rate (r) is determined as b = 1 + r.
The decay rate (r) is determined as b = 1 - r.
y = ab^x (Where b = 1 - r)
y = a(1-r)^x
a represents the initial value
r represents growth or decay rate
x represents the number of time intervals that have passed.
<em>For example</em>
The population of Home Town is 2016 was estimated to be 35,000 people with an annual rate of increase of 2.4%.
The equation for decay factor y = 35000(1 - 0.024)^x
y = 35000(0.976). (where x = 1)
- Key -
Black tiles = x
Purple tiles = x+50
Yellow tiles = 5x
-
Total = x + x+50 + 5x = 400
⇒ 7x + 50 = 400
⇒ 7x = 400-50 = 350
⇒ x = 350/7
⇒ x = 50
Black tiles = 50
Purple tiles = 50+50 = 100
Yellow tiles = 5 x 50 = 250
Answer:
-Exponential Decay
-Decay factor is (1-0.05)
Step-by-step explanation:
-Given that the number decreases by a defined rate each year from the initial size by 5%,
-This is an exponential decay function of the form:
Where:
is the quantity/size after time t
is the initial size
is the rate of decay
-Our function can the be written as
Hence, the decay rate/factor is 0.05
#Alternatively
The exponential decay can be of the form:
Where:
y is the size at time x, a is the initial size, x is time and b is the decay factor.
b is of the form 
Hence, the decay factor is (1-0.05)
