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Sagot :
Answer:
- y = 5*2ˣ
Step-by-step explanation:
Exponential function:
- y = abˣ
Ordered pairs given:
- (1, 10) and (4, 80)
Substitute x and y values to get below system:
- 10 = ab
- 80 = ab⁴
Divide the second equation by the first one and solve for b:
- 80/10 = b³
- b³ = 8
- b = ∛8
- b = 2
Use the first equation and find the value of a:
- 10 = a*2
- a = 5
The function is:
- y = 5*2ˣ
Answer:
[tex]y=5 \cdot 2^x[/tex]
Step-by-step explanation:
An exponential function is written in the form:
- [tex]y=ab^x[/tex]
We can use the given points that the exponential function passes through to solve for a and b.
Create a system of equations by substituting (1, 10) and (4, 80) into the exponential form of a function.
- [tex]\text{I}:\ 10=ab^1[/tex]
- [tex]\text{II}: \ 8 0=ab^4[/tex]
Divide Equation I by Equation II in order to cancel out variable a.
- [tex]\displaystyle \frac{80=ab^4}{10=ab}[/tex]
- [tex]8=b^3[/tex]
- [tex]b=2[/tex]
Now we can solve for a by substituting b back into either equation from the system of equations.
- [tex]10=ab[/tex]
- [tex]10=a(2)[/tex]
- [tex]a=5[/tex]
Substitute 5 for a and 2 for b into the form of an exponential function to find the exponential function that passes through (1, 10) and (4, 80).
- [tex]y=5 \cdot 2^x[/tex]
y = 5 · 2ˣ is the exponential function that describes the graph.
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