NZ Level 7 (NZC) Level 2 (NCEA)
Transforming Exponential Expressions

## Interactive practice questions

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(1r)t, where $r$r is a decimal.

c

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

growth

A

decay

B

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 $\frac{t}{1602}$t1602 years is given by $A=k\left(\frac{1}{2}\right)^{\frac{t}{1602}}$A=k(12)t1602.

### Outcomes

#### M7-6

Manipulate rational, exponential, and logarithmic algebraic expressions

#### 91261

Apply algebraic methods in solving problems