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Answer:
y = 17*(3)ˣ
Step-by-step explanation:
y=abˣ
(0,17) : 17 = a*b⁰ = a
(2,153) : 153 = a*b² = 17*b²
b² = 153/17 = 9
b = ± 3 ... (0,17) and (2,153) in first quadrant b = 3
function: y = 17*(3)ˣ
y = 17([tex]3^x[/tex]) is the needed exponential function that runs across locations (0, 17) and (2, 153).
Exponential Function:
The Exponential Function is a mathematical function that describes the relationship between two variables.
The real-valued function is always positive. e^x is the most well-known exponential function, with e as the base and x as the exponent.
Let y = ab^x be the necessary exponential function.
We must now use the supplied circumstances to determine constants A and k.
Due to the fact that this exponential function goes through the position (0, 17)
Therefore
3 = ab^0
a = 17
In addition, the exponential function goes through the point (2, 153)
Therefore
153 = a b^2
Substitute the value of a
17b^2 = 153
b^2 = 9
b = ±3
Since b is base of the exponential function and base can not be negative for that therefore
b = 3
We now have an exponential function equation with these values.
y = 17(3^x)
This is the required exponential function.
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