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timama [110]
3 years ago
13

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 20)(0,20) and (6, 1280)(6,1280).

Mathematics
1 answer:
Phoenix [80]3 years ago
8 0

Answer:

y=20(2)^x

Step-by-step explanation:

We want to write an exponential function that goes through the points (0, 20) and (6, 1280).

The standard exponential function is given by:

y=ab^x

The point (0, 20) tells us that <em>y</em> = 20 when <em>x</em> = 0. Hence:

20=a(b)^0

Simplify:

20=a(1)\Rightarrow a=20

So, our exponential function is now:

y=20(b)^x

Next, the point (6, 1280) tells us that <em>y</em> = 1280 when <em>x</em> = 6. Thus:

1280=20(b)^6

Solve for <em>b</em>. Divide both sides by 20:

64=b^6

Therefore:

b=\sqrt[6]{64}=2

Hence, our function is:

y=20(2)^x

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