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

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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Step-by-step explanation:

Given

Required

Determine the exponential function

In

and

Substitute these values in

--- (1)

In

and

Substitute these values in

--- (2)

Divide (2) by (1)

Apply second law of indices

Express 64 as an exponent of 3

Substitute 4 for b in (1)

Solve for a

Substitute 1 for a and 4 for b in

$450 is the answer.

step-by-step explanation:

30% of 450 = 135

450-135=315