meredith48034
contestada

NO LINKS!! Part 1
Find an exponential function in y = ab^x form that satisfies the given information :

a. Has y-int (0, 2) and has a multiplier of 0.8

b. passes through the points (0, 3.5) and (2, 31.5)

Respuesta :

mhanifa

Answer:

  • A) y = 2*0.8ˣ
  • B) y = 3.5*3ˣ

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Part A

Use the coordinates to determine the function.

Point (0, 2):

  • 2 = a*b⁰ ⇒ 2 = a

The function becomes:

  • y = 2bˣ

It has a multiplier of 0.8, so b = 0.8, so the function is:

  • y = 2*0.8ˣ

Part B

Use the first point:

  • 3.5 = a*b⁰ ⇒ 3.5 = a

Use the second point:

  • 31.5 = 3.5*b²
  • 9 = b²
  • b = √9
  • b = 3

The function is:

  • y = 3.5*3ˣ
semsee45

Answer:

[tex]\textsf{a)} \quad y=2(0.8)^x[/tex]

[tex]\text{b)} \quad y=3.5(3)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Question (a)

Given:

  • y-intercept = (0, 2) ⇒ a = 2
  • multiplier = 0.8 ⇒ b = 0.8

Substitute the values of a and b into the exponential function formula:

[tex]\implies y=2(0.8)^x[/tex]

Question (b)

The y-intercept is when x = 0.  Therefore, given the function passes through point (0, 3.5), the y-intercept is 0.35 ⇒ a = 3.5.

Substitute the found value of a and given point (2, 31.5) into the exponential function formula and solve for b:

[tex]\implies 31.5=3.5b^2[/tex]

[tex]\implies b^2=9[/tex]

[tex]\implies b=3[/tex]

Substitute the values of a and b into the exponential function formula:

[tex]\implies y=3.5(3)^x[/tex]

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