U4L7 Mixture of Growth and Decay Practice

The formula for exponential growth is $$y = a(1 + r)^t$$ , where 'a' is the initial amount, 'r' is the growth rate, and 't' is the time.

'r' represents the growth rate expressed as a decimal. For example, a 5% growth rate is represented as 0.05.

To convert a percentage to a decimal, divide the percentage by 100. For example, 5% becomes 0.05.

The common ratio 'b' in the function is 1.16.

To write an exponential growth function, use the formula $$y = a(1 + r)^t$$ , where 'a' is the initial value and 'r' is the growth rate.

The exponential growth function is $$y = 8000(1.06)^t$$ .

After 1 year, the value of the painting is $$y = 1400(1.09)^1 = 1526$$ .

To calculate the population after 't' years, substitute 't' into the exponential growth function $$y = a(1 + r)^t$$ .

Exponential growth increases over time, while exponential decay decreases over time. The formulas are $$y = a(1 + r)^t$$ for growth and $$y = a(1 - r)^t$$ for decay.

You plug in 0.05 for 'r' in the exponential growth formula.