Answer:
f(x) = 3(2)^x
Step-by-step explanation:
The Table is:
<u>x</u> <u>f(x)</u>
-2 3/4
-1 3/2
0 3
1 6
2 12
The exponential funtion has the next form:
f(x) = a(b)^x
At x = 0, f(x) = a. Then, a = 3
Isolating b from the equation:
f(x)/a = b^x
ln(f(x)/a) = x*ln(b)
[ln(f(x)/a)]/x = ln(b)
At x = 1, f(x) = 6. Then:
[ln(6/3)]/1 = ln(b)
ln(2) = ln(b)
2 = b
Therefore, the function is f(x) = 3(2)^x
Answer:
the area of the garden is 9 square kilometers
Step-by-step explanation:
4s=12
s=3
A= 3*3 = 9
Answer:
Volume of the right pyramid = 288 m²
Step-by-step explanation:
Volume of the pyramid = 
From the ΔAOB,
By Pythagoras theorem,
AB² = AO² + OB²
(6√2)² = AO² + (6)²
72 = AO² + 36
AO = √(36) = 6 m
Since base of the pyramid is a square so area of the base = (Length × Width) = (side)²
Now volume of the pyramid = ![\frac{1}{3}[(Length)(width)]\times height](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5B%28Length%29%28width%29%5D%5Ctimes%20height)
= 
= 288 m²
Therefore, volume of the right pyramid is 288 m².
Answer:
Area of table cloth = 49/9 m² or 5.44 m²
Step-by-step explanation:
Given:
Side of table cloth =
= 7/3 m
Shape of cloth is square
Find:
Area of table cloth
Computation:
Area of square = side²
So,
Area of table cloth = side²
Area of table cloth = (7/3)²
Area of table cloth = 49/9 m² or 5.44 m²
The mileage from the Supermarket to the Library may be calculated using Pythagorean Theorem.
The coordinates of the Library are (7,10) and the coordinates of the Supermarket are (3,7).
So, the distance requested is √ [ (7-3)^2 + (10 - 7)^2 = √[ 4^2 + 3^2 = √ [16 + 9] =
= √25 = 5
So, he runs 5 miles.
And the reimbursement will be $0.50 / mile * 5 mile = $ 2.50.
Answer: option B) $ 2.50