Mathematics: Find the equation of the exponential function, in y=a(b)^x form that passes through the points (-2,3) and (6,35). round both a and b to the nearest hundredth. must be an algebraic method.

Find the equation of the exponential function,

Ответ:

sulemmaa

17.01.2022

I supose your function is: $y(x)=a \cdot b^x$

Step 1. Replace the coordinates of the first point in your equation:
x=-2, y=3

$3=a \cdot b^{-2}$

Solve the equation for "a":
$a=3 \cdot b^2$

Step 2. Replace the coordinates of the second point in your equation:
x=6, y=35

$35 = a \cdot b^6$

Replace the value of "a" from Step 1.
$35 = 3 \cdot b^2 \cdot b^6$
Calculate "b":
$b= \sqrt[8]{\frac{35}{3}} = 1.359466$

Step 3. Replace "b" in first equation and calculate "a":
$a=3 \cdot b^2=5.5444434$

The equation is:
$y(x)=5.54 \cdot 1.36^x$

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Ответ:

brandiwingard

12.09.2020

Mathematics

x=-5.333333

Step-by-step explanation:

The sum of three-fourths of a number

Let the number be x

3/4 of the number

3/4 of x

3/4(x)

3x/4

The sum of 3x/4 and 1 is negative 5

3x/4-1=-5

Make 3x/4 the subject

3x/4=-5+1

3x/4=-4

Cross multiply

3x=-4(4)

3x=-16

x=-16/3

x=-5.333333

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Find the equation of the exponential function, in y=a(b)^x form that passes through the points (-2,3) and (6,35). round both a and b to the nearest hundredth. must be an algebraic method.

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