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Grade 12

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
d

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

Easy
2min

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.

Easy
2min

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

Easy
1min

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.

Easy
4min
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Outcomes

12CT.A.1.3

Determine, through investigation using graphing technology, the point of intersection of the graphs of two exponential functions (e.g., y = 4^-x and y = 8^(x+3) ), recognize the x-coordinate of this point to be the solution to the corresponding exponential equation (e.g., 4^x = 8^(x+3) ), and solve exponential equations graphically

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