Answer:
Step-by-step explanation:
<u>Exponential Growth</u>
The natural growth of some magnitudes can be modeled by the equation:
Where P(t) is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.
It's given the annual sales for a surf shop are Po=$130,000. They are increasing at a rate of r=7% = 0.07 per year. Substituting values, the function is:
The value of the function after t=7 years is
Computing:
Answer:
3
Step-by-step explanation:
Answer:
a = 7 and b = - 18
Step-by-step explanation:
If (x - 1) is a factor of f(x) then x = 1 is a root and f(1) = 0, thus
f(1) = 1³ + 10(1)² + a + b = 0 and
1 + 10 + a + b = 0 ⇒ a + b = - 11 → (1)
Similarly if
(x + 2) is a factor then x = - 2 is a root and f(- 2) = 0
f(- 2) = (- 2)³ + 10(- 2)² - 2a + b = 0, thus
- 8 + 40 - 2a + b = 0 ⇒ - 2a + b = - 32 → (2)
Solve (1) and (2) simultaneously
Subtract (1) from (2)
- 3a = - 21 ( divide both sides by 3)
a = 7
Substitute a = 7 in (1)
7 + b = - 11 ⇒ b = - 11 - 7 = - 18
The required polynomial is
f(x) = x³ + 10x² + 7x - 18
Let *s* be the length of the side of the square and *h* be the length of the side of the hexagon
s=h+5
4s=6h
multiply the fisrt equation by 4
4s=4h+20
4s=6h
4h+20=6h
20=2h
h=10
s=h+5
s=10+5
s=15
This sequence starts with an initial set; let’s call it s1. This set contains 20 cans, and every set following would have two less cans than the last set. So,
s1=20
s2=s1-2=18
s3=s2-2=16
•
•
•
s9=s8-2=4
How many cans in the display represents the value of each set added together, so we can denote this as
s1+s2+s3+...+s9
and replacing with values:
20+18+16+...+4 = 108
The number of cans in the display equals 108.
(The set notation seems weird, but by practicing this application now, the Calculus version will seem easier.)