Question 1
- Thread starter Emma890
- Start date
To help you understand how to proceed let’s try replacing a and b with numbers.
Let’s work out two points on the curve y = 9(3ˣ).
To work out y value when x = 0 sub x = 0 into rule and solve for y:
y = 9(3⁰)
⇒ y = 9
To work out y value when x = 2 sub x = 2 into rule and solve for y:
y = 9(3²)
⇒ y = 81
The curve y = 9(3ˣ) passes through (0,9) and (2,81).
Now what if we don’t know the values of a and b in the rule y = a(bˣ) but are given two points
through which the curve passes?
Can we work back to find values of a and b?
Use (2,81) to write 81 = a(b²) (replacing x with 2 and y with 81).
Use (0,9) to write 9 = a(b⁰) (replacing x with 0 and y with 9)
9 = a(b⁰) becomes
9 = a since b⁰ = 1
Replacing a with 9 in 81 = a(b²) gives:
81 = 9(b²)
⇒ b² = 9
⇒ b = 3
Therefore rule is y = 9(3ˣ)
By changing 9 to index form (9 = 3²) we can write:
y = 3² × 3ˣ
⇒ y = 3ˣ⁺²
So now have a go at your question - at least post an attempt so we can see where you are getting stuck.
Let’s work out two points on the curve y = 9(3ˣ).
To work out y value when x = 0 sub x = 0 into rule and solve for y:
y = 9(3⁰)
⇒ y = 9
To work out y value when x = 2 sub x = 2 into rule and solve for y:
y = 9(3²)
⇒ y = 81
The curve y = 9(3ˣ) passes through (0,9) and (2,81).
Now what if we don’t know the values of a and b in the rule y = a(bˣ) but are given two points
through which the curve passes?
Can we work back to find values of a and b?
Use (2,81) to write 81 = a(b²) (replacing x with 2 and y with 81).
Use (0,9) to write 9 = a(b⁰) (replacing x with 0 and y with 9)
9 = a(b⁰) becomes
9 = a since b⁰ = 1
Replacing a with 9 in 81 = a(b²) gives:
81 = 9(b²)
⇒ b² = 9
⇒ b = 3
Therefore rule is y = 9(3ˣ)
By changing 9 to index form (9 = 3²) we can write:
y = 3² × 3ˣ
⇒ y = 3ˣ⁺²
So now have a go at your question - at least post an attempt so we can see where you are getting stuck.
Otis
Elite Member
- Joined
- Apr 22, 2015
- Messages
- 4,592
Hi Emma. Did you try to find values for a and b, first, as they suggested?
If you need help with that part, start by substituting the given (x,y) coordinates for point A into the equation y=a·bx.
8 = a·b0
They reminded you what b0 is, so substitute that value for b0. This leads to the value for a.
Next, substitute the value for a, along with the (x,y) coordinates for point B, into the equation y=a·bx. Solve for b.
Please show us how far you get, on this first part.
?
If you need help with that part, start by substituting the given (x,y) coordinates for point A into the equation y=a·bx.
8 = a·b0
They reminded you what b0 is, so substitute that value for b0. This leads to the value for a.
Next, substitute the value for a, along with the (x,y) coordinates for point B, into the equation y=a·bx. Solve for b.
Please show us how far you get, on this first part.
?