Question

What is the rate of growth or decay in the equation
y = 1600(88)×

Answer 1

Rate of growth = 88

Initial value = 1600

Explanation:

The given equation is an exponential function.

What is an exponential function?

An exponential function is used to calculate the exponential growth or decay of a given set of data. In an exponential function, the variable is the exponent.

`\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}}`

Given equation:

`y=1600(88)^x`

The given equation is an exponential function where:

• a = 1600
• b = 88

Therefore, the initial value of the equation is 1600.

As b > 1, the function represents exponential growth, and the growth factor is 88. This means that for each increase of one unit in the independent variable (x), the dependent variable (y) will be multiplied by 88.