Mathematics, 30.11.2020 09:00 alanflores40

Use substitution to find an exponential function, y= a - b" that passes through (2, 16) and (5, 1.024).

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Answer from: markleal4022

The exponential function is given by y = 100(0.4)ˣ

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the factor.

At point (2, 16):

16 = ab² (1)

At point (5, 1.024):

1.024 = ab⁵ (2)

Dividing equation 2 by equation 1:

b³ = 0.064

b = 0.4

16 = a(0.4)²

a = 100

The exponential function is given by: y = 100(0.4)ˣ

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Answer from: Aaraar

y = 4^x

Step-by-step explanation:

Given

(2,16)

(5,1,024)

Required

Determine the exponential function y = a.b^x

In (2,16)

x=2 and y = 16

Substitute these values in y = a.b^x

16 = a.b^2 --- (1)

In (5,1,024)

x = 5 and y = 1024

Substitute these values in y = a.b^x

1024 = a.b^5 --- (2)

Divide (2) by (1)

$\frac{1024}{16} = \frac{a.b^5}{a.b^2}$

$\frac{1024}{16} = \frac{b^5}{b^2}$

$64 = \frac{b^5}{b^2}$

Apply second law of indices

$64 = b^{5-2$

64 = b^3

Express 64 as an exponent of 3

4^3 = b^3

4 = b

b = 4

Substitute 4 for b in (1)

16 = a.b^2

16 = a * 4^2

16 = a * 16

16 = 16a

Solve for a

$a=\frac{16}{16}$

a = 1

Substitute 1 for a and 4 for b in y = a.b^x

y = 1 * 4^x

y = 4^x

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

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Use substitution to find an exponential function, y= a - b" that passes through (2, 16) and (5, 1.0...