Exponentials

Hong Kong

Stage 4 - Stage 5

Consider the function $f\left(t\right)=2\left(\frac{3}{8}\right)^t$`f`(`t`)=2(38)`t`, where $t$`t` represents time.

a

What is the initial value of the function?

b

Express the function in the form $f\left(t\right)=2\left(1-r\right)^t$`f`(`t`)=2(1−`r`)`t`, where $r$`r` is a decimal.

c

Does the function represent growth or decay of an amount over time?

growth

A

decay

B

d

What is the rate of decay per time period? Give the rate as a percentage.

Easy

Approx 2 minutes

Consider the function $f\left(t\right)=\frac{8}{7}\left(\frac{3}{8}\right)^t$`f`(`t`)=87(38)`t`, where $t$`t` represents time.

Consider the function $f\left(t\right)=\frac{5}{6}\left(2\right)^t$`f`(`t`)=56(2)`t`, where $t$`t` represents time.

Starting at $k$`k` grams, the amount of radium-226 in a sample after $\frac{t}{1602}$`t`1602 years is given by $A=k\left(\frac{1}{2}\right)^{\frac{t}{1602}}$`A`=`k`(12)`t`1602.

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