Ms. Terkper's Digital Classroom

Exponential & Logarithmic Functions (Math 30-1)

Dive into exponential growth and decay, logarithms, laws of logs, and graphing techniques.

Exponential \(y=a\,b^{\,m(x-h)}+k\) Logarithmic \(y=a\,\log_b(m(x-h))+k\) Growth/Decay \(A=A_0(1+p)^n,\ A=A_0e^{kn}\) Laws: \(\log_b(MN)=\log_b M+\log_b N\)

What You Should Be Able To Do

Model contexts with \(A=A_0(1+p)^n\) and \(A=A_0e^{kn}\); interpret growth factor, doubling/half-life.
Evaluate and simplify logs using change of base and laws of logarithms.
Solve exponential/log equations using algebra and logarithms.
Graph \(y=a\,b^{\,m(x-h)}+k\) and \(y=a\,\log_b(m(x-h))+k\) and identify asymptotes and key points.

I can build growth/decay models from context. I can use change of base and log laws correctly. I can solve exponential/log equations for an unknown. I can graph and describe transformations and asymptotes. Progress autosaves to this device.

Video Library

Growth & Decay (Discrete vs Continuous)

From \(A=A_0(1+p)^n\) to \(A=A_0e^{kn}\), doubling & half-life.

youtube.com – “exponential growth and decay discrete continuous”

Laws of Logarithms & Change of Base

Product, quotient, power rules; \(\log_b x=\frac{\ln x}{\ln b}\).

youtube.com – “laws of logarithms change of base”

Solving Exponential Equations with Logs

Common base, natural logs, isolating the exponent.

youtube.com – “solving exponential equations with logs”

Graphing Logarithms & Transformations

Vertical asymptotes, reflections, stretches, shifts.

youtube.com – “graphing logarithmic functions transformations”

Interactive Tools

Graph Explorer

Type

a

base \(b\) ( \(b>0, b\neq1\) )

m (horizontal scale)

h (right +)

k (up +)

Parent Transformed Asymptote

Growth/Decay Modeler

Mode Initial \(A_0\)

Percent per step \(p\) (e.g., 5 for +5, −12 for −12)

Steps \(n\)

Log & Exponential Solver

Change of base: compute \(\log_b(x)=\frac{\ln x}{\ln b}\)

Solve \(b^{c x+d}=y\) for \(x\)

Solve for \(t\) in \(A=A_0(1+p)^t\)

Solve for \(t\) or \(k\) in \(A=A_0 e^{k t}\)

Quizzes

Quiz 1: Growth/Decay & Exponential Equations

Discrete vs continuous models; solving with logs.

Quiz 2: Logs, Laws & Graphs

Change of base, log laws, graphing with transformations.

Downloadable Review

Quick Practice Scratchpad

Try: Find \(t\) if \(A_0=500\), \(A=800\), \(p=6\%\). Evaluate \(\log_{3}(81)\). Graph \(y=2\cdot 3^{-(x-1)}-4\).