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Nit.
junesk 12 ors bookmaiks
Mure Menu Stufi
DragenFly MAX

Drift Hunters
witlon
iestion 2 of 10
Write the equation for an exponential function, in the form
y=a ×b^(x), whose graph passes throt coordinate points
(1,7.5) and
(3,16.875).

Nit. $\newline$ junesk $12$ ors bookmaiks $\newline$ Mure Menu Stufi $\newline$ DragenFly MAX $\newline$ - Drift Hunters $\newline$ witlon $\newline$ iestion $2$ of $10$ $\newline$ Write the equation for an exponential function, in the form $y=a \times b^{x}$ , whose graph passes throt coordinate points $(1,7.5)$ and $(3,16.875)$ .

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Convert between exponential and logarithmic form: all bases

Full solution

Q. Nit.

\newline

junesk

12

ors bookmaiks

\newline

Mure Menu Stufi

\newline

DragenFly MAX

\newline

- Drift Hunters

\newline

witlon

\newline

iestion

2

of

10

\newline

Write the equation for an exponential function, in the form

y=a \times b^{x}

, whose graph passes throt coordinate points

(1,7.5)

and

(3,16.875)

.

General Form Identification: First, let's use the general form of an exponential function, $y = a \cdot b^x$ . We need to find the values of $a$ and $b$ that will make the function pass through the points $(1,7.5)$ and $(3,16.875)$ .
First Point Calculation: Plug in the coordinates of the first point $(1,7.5)$ into the equation to get $7.5 = a \cdot b^1$ , which simplifies to $7.5 = a \cdot b$ .
Second Point Calculation: Now plug in the coordinates of the second point $(3,16.875)$ into the equation to get $16.875 = a \cdot b^3$ .
Elimination of Variable: We now have two equations: $7.5 = a \times b$ and $16.875 = a \times b^3$ . We can divide the second equation by the first to eliminate $a$ and solve for $b$ . So, $(16.875 / 7.5) = b^3 / b$ , which simplifies to $2.25 = b^2$ .
Finding Value of $b$ : To find $b$ , we take the square root of $2.25$ , which gives us $b = 1.5$ .
Substitute $b$ to Find $a$ : Now that we have $b$ , we can substitute it back into the first equation $7.5 = a \times b$ to find $a$ . So, $7.5 = a \times 1.5$ .
Final Exponential Function: Divide both sides by $1.5$ to solve for $a$ , which gives us $a = \frac{7.5}{1.5}$ . This simplifies to $a = 5$ .
Final Exponential Function: Divide both sides by $1.5$ to solve for $a$ , which gives us $a = \frac{7.5}{1.5}$ . This simplifies to $a = 5$ . Now we have both $a$ and $b$ , so the exponential function is $y = 5 \times 1.5^x$ .

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