Question

NO LINKS!! URGENT HELP PLEASE!!

#23 & 24: Please help me ​

Answer 1

`\textsf{23)} \quad y=3\left((5)/(3)\right)^x`

`\textsf{24)} \quady=2\left((1)/(2)\right)^x`

Explanation:

The general formula for an exponential function is:

`\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}}`

Question 23

From inspection of the given graph, the exponential curve passes through the points (0, 3) and (1, 5).

The y-intercept is the value of y when x = 0. Therefore, a = 3.

To find the value of b, substitute point (1, 5) and the found value of a into the exponential function formula:

`\begin{aligned}y&=ab^x\\\\\implies 5&=3b^1\\\\5&=3b\\\\b&=(5)/(3)\end{aligned}`

To write an equation for the graphed exponential function, substitute the found values of a and b into the formula:

`\boxed{y=3\left((5)/(3)\right)^x}`

`\hrulefill`

Question 24

From inspection of the given graph, the exponential curve passes through points (-1, 4) and (0, 2).

The y-intercept is the value of y when x = 0. Therefore, a = 2.

To find the value of b, substitute point (-1, 4) and the found value of a into the exponential function formula:

`\begin{aligned}y&=ab^x\\\\\implies 4&=2b^(-1)\\\\2&=b^(-1)\\\\2&=(1)/(b)\\\\b&=(1)/(2)\end{aligned}`

To write an equation for the graphed exponential function, substitute the found values of a and b into the formula:

`\boxed{y=2\left((1)/(2)\right)^x}`