Graph the exponential model !!! Help needed !!!
2 answers:
Answer:
Point (1 , 0.75) lies on the graph of the function ⇒ last answer
Step-by-step explanation:
* Lets revise the exponential function
- An exponential function with base b is defined by f (x) = ab^x
where a ≠0, b > 0 , b ≠1, and x is any real number.
- The base, b, is constant and the exponent, x, is a variable.
- The graph of it in the attached figure
- Features (for this graph):
• The domain is all Real numbers.
• The range is all positive real numbers (not zero).
• The y-intercept at (0 , 1.5). Remember any number to
the power of zero is 1.
• Because 0 < b < 1, the graph decreases (b = 1/2)
* Now lets check which point lies on the graph
- Substitute the value of x of the point, in the function
- If the answer is the same as y, then the point lies on the graph of
the function
∵ y = 1.5(1/2)^x
∵ x = -3
∴ y = 1.5(1/2)^(-3) = 187.5 ≠ 1
∴ Point (-3 , 1) does not lie on the graph of the function
∵ x = 2
∴ y = 1.5(1/2)² = 3/8 ≠ 5
∴ Point (2 , 5) does not lie on the graph of the function
∵ x = -2
∴ y = 1.5(1/2)^-2 = 6 ≠ 3
∴ Point (-2 , 3) does not lie on the graph of the function
∵ x = 1
∴ y = 1.5(1/2)^1 = 0.75
∴ Point (1 , 0.75) lies on the graph of the function
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Answer:
You have 15 dimes. You have 9 quarters. You have 12 nickels
Step-by-step explanation:
lets set some variables:
let "n" = the number of nickels
let "d" = the number of dimes
let "q" = the number of quarters
So, the total amount of money you have should be: $4.35 = 0.25q + 0.10d + 0.05n
Now let's look at the relationships between the coins:
"There are three fewer quarters than nickels": n - 3 = q
"six more dimes than quarters": q + 6 = d
So now you have three equations with three variables, all you need to do is solve.
first, you can substitute "n-3" for "q" (according to the 2nd equation) in the 1st and 3rd equation, you get:
You now only have two equations and two variables.
Simplify:
Now substitute "n+3" for "d" (according to the 2nd equation) in the 1st equation:
4.35=0.30n-0.75+0.10(n+3)
simplify:
4.35=0.30n-0.75+0.10n+0.30
4.35=0.40n-0.45
4.35+0.45=0.40n
4.80=0.40n
n=12
You have 12 nickels. Now sub "n" back into your equations to find the number of dimes and quarters:
n - 3 = q
12 - 3 = q
q = 9
You have 9 quarters.
q + 6 = d
9 + 6 = d
d = 15
You have 15 dimes.