March 13 (Exercises 5.3 Worksheet)

March 13

So Tuesday's class we mainly went over our homework problems on Exponential Functions. (look back at phoebes blog of 3/7-3/8 if you need to review that.)

We did problems 7, 9, 11, 13, 14, 43, 44, and 58 for homework.
In problems 7, 9 and 11 we needed to name the transformations that were needed to transform the graph of h(x)=2^x into the given.
7. f(x) = 2^x - 5 --> Vertical Shift
9. k(x) = 3(2^x) --> Vertical Stretch
11. f(x) = 2(x+2)-5 --> Horizontal Shift (to left) and Vertical Shift (5 units down)

In problems 13, and 14 we had to match each function to the graphs that were given.
13.
f(x) = a^x       --> C
g(x) = a^x+ 3   --> A
h(x) = a^(x+5) --> B

14.
f(x) = c^x     -->B
g(x) = -3c^x  ---> C
h(x) = c(x+5)   --> A
k(x) = -3c^x-2 ---> D

43.

44.

 58.

Find an exponential function that goes through these points
 Ex#1
(0, 5), (2, 45)

y = a*b^x
y = 5b^x

Plug In!! :
 45=5b^2 --> b=3

Answer: y = 5 * 3^x

Ex#2
(1, 4), (5, 1/4) --> Decay!
y = a*b^x

For (1, 4): 4= a *b^1 --> 4/b=a
For (5, 1/4): 1/4=a*b^5

plug in --> 1/4= 4/b*b^5/1 --> 1/4= 4b^4/1 -->16b^4=1 --> b^4=1/16 --> b=1/2

Answer: y= a*1/2^x (this makes sense because it's decreasing)