Chapter 2
Models of Growth: Rates of Change
2.4
Exponential Functions
Exercises
- Suppose you invest `\$`4000 at an annual interest rate of 5.25% compounded annually. How much would you have in 20 years?
- How much would you have to invest at 4.75% compounded annually so that you would have `\$`20,000 after 10 years?
- How much would you have to invest at 5.15% compounded annually so that you would have `\$`30,000 after 20 years?
- Rewrite each of the following equations in exponential form.
a. `log_9 3=1/2` b. `log_10 1000=3` c. `log_10 0.1=-1` d. `log_2 4=2` e. `log_10 100=2` f. `log_10 0.01=-2` -
Find the value of each of the following expressions.
a. `ln 1` b. `ln e` c. `ln e^3` d. `ln e^2.7183` e. `ln 1/e` f. `ln 1/e^2` -
Solve each of the following equations for `t`.
a. `t^6=10` b. `e^t=10` c. `10^t=6` -
Calculate each of the following derivatives.
a. `d/(dt) e^(-2t)` b. `d/(dt) e^(0.07t)` c. `d/(dt) 2^t` d. `d/(dt) (2t-5e^t)` e. `d/(dt) 4t^3` f. `d/(dt) e` - Express `2e^(3t)` in the form `c b^t`.
- Express `15e^(0.15t)` in the form `c b^t`.
- Express `2*3^t` in the form `c e^(kt)`.
- Express `3*10^t` in the form `c e^(kt)`.
- Find the derivative of each of the following functions.
a. `t^4-2t^3+2t^2-t-1` b. `t^5+t^3-t^2-9+e^(-t//3)` c. `4 e^4-3 e^3+2 e^2-e+7` d. `13-26t +6t^2+e^t` e. `2 e^(3t)-3t^2` f. `1/(e^(2t))` g. `t^10+10^t` h. `2/10^t`
-
Find the slope of the graph of `y=e^t` at each of the following points.
a. `text[(]2,e^2text[)]` b. `text[(]-2,e^-2text[)]` -
Find the slope of the graph of `y=2^t` at each of the following points.
a. `text[(]2,4text[)]` b. `text[(]-2,0.25text[)]` -
Find the slope of the graph of `y=10^t` at each of the following points.
a. `text[(]2,100text[)]` b. `text[(]-2,0.01text[)]` -
Find the slope of the graph of `y=3^t` at each of the following points.
a. `text[(]2,9text[)]` b. `text[(]-2,1text[/]9text[)]`
