Question

write an exponential function y=ab^x whose graph passes through the points (1,3) and (2,12)


y = ?

Answer 1

Answer:

y=3/4(4)^x

Step-by-step explanation:

hello :

the graph passes through the point (1,3) : when x=1  and  y=3  : 3= ab^1

the graph passes through the point (2,12) : when x=2  and  y=12  : 12= ab^2

so the system :  ab=3 ...(*)

                         ab² =12..(**)

ab² = b(ab) = 12   but : ab=3    so : (**) equivalent to     b(3)=12  .... b=12/3=4

now : ab= 3 and b=4    so : 4a=3  ... a=3/4

y=3/4(4)^x

Answer 2

The exponential function that passes through (1,3) and (2,12) is y = 0.75 * 4^x

How to determine the exponential function?

The points on the function are given as:

(1,3) and (2,12)

The equation of the function is:

y = ab^x

At (1,3), we have:

ab^1 = 3

ab = 3

At (2,12), we have:

ab^2 = 12

Divide both equations

ab^2/ab =12/3

This gives

b = 4

Substitute b = 4 in ab = 3

4a = 3

Divide by 4

a = 0.75

Substitute b = 4 and a = 0.75 in y = ab^x

y = 0.75 * 4^x

Hence, the exponential function is y = 0.75 * 4^x

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