1. Ch 5 Review

2. 5.1- Interest formulas Simple Interest: A = P + P x r x n
Arithmetic sequences
Linear functions
A loan for $50,000 accrues 5% interest per year
F(n)= x 0.05 x n
Compound Interest: 𝐴=𝑃 (1+𝑟) 𝑛
Geometic sequences
Exponential functions
A loan for $50,000 accrues 5% compound interest per year
F(n)=50000 (1+0.05) 𝑛 n
F(n)
50000 1
52500 2
55000 3
57500 4
60000 n
F(n)
50000 1
52500 2
55125 3 4
Ex: How much do you have after 3 years with a savings account with $120,000 that earns 2%compounded interest?
Ex: How much do you pay after 6 years for an $80,000 loan with a 4.125% simple interest rate?

3. 5.2 Exponential Functions: 𝑦=𝑎∗ 𝑏 𝑥 a is the y-intercept because
the y- intercept is where x = 0
𝑦=𝑎∗ 𝑏 0
𝑦=𝑎∗1
𝑦=𝑎
Exponential functions have horizontal asymptotes – a horizontal line that the function gets very close to but never actually crosses. The HA here is y = 0 x Y 5 1 10 2 20 3 40
We can find the exponential function given a table or graph.
A = 5 because it is the y-intercept so we know
𝑦=5∗ 𝑏 𝑥 Then we can use any other point to find b:
Using the point (1, 10) plug in 1 for x and 10 for y
10=5∗ 𝑏 1
Now solve for b
2= 𝑏 1 so b = 2
The function is y=5∗ 2 𝑥

4. 5.6- Solving Exponential equations
Graphing:
y = 3∗ 4 𝑥 a curve
y = 48 a horizontal line
The intersection point is the solution
Given the equation 3∗ 4 𝑥 =48, solve for x
Use the graph
Or solve algebraically
Algebraically:
1. Isolate the exponential term
3∗ 4 𝑥 =48
divide both sides by 3
4 𝑥 =16
2. Re-write each side as an exponential expression with the same base
4 𝑥 = 4 2
3. Set exponents equal to each other
𝑥=2
4. Solve for x if necessary
5. Check answer
To find intersection on calculator
Type functions into y=
Hit 2nd, calc
Choose #5
Enter, enter, enter
Example:
Use either method to solve 2∗ 5 𝑥−1 =250