Homework 4.2

1.  If f​(x)=

​, find f​(3​) and f​(−3​).

f(3)=

f(-3)=

2. Solve the equation for x.

${\left(\frac{1}{4}\right)}^x=1024$

The solution set is

3.  Solve the equation.

$r^{4/3}=81$

The solution set is

4.  Solve the equation.

$A=6000 {\left(1+\frac{0.05}{2}\right)}^{6\left(2\right)}$

$A\approx$

5.  Solve the given equation.

$8000=4000{\left(1+r\right)}^{24}$

$r\approx$

6. If f​(x)=

​, find f​(1​).

7.  For f(x)=

, find

.

8.  Graph the equation.

$y={\left(\frac{4}{3}\right)}^x$

9.  Graph the following function. 

Choose the correct graph below.

10.  Graph the equation on​ paper, and then choose the correct graph. 

Choose the correct graph on the right.

11. Solve the equation.

The solution set is

12. Solve the equation for x.

${\left(\frac{2}{5}\right)}^x=\left(\frac{125}{8}\right)$

The solution set is

13. Solve the equation analytically. 

The solution set is

14   Solve the equation. 

The solution set is

15.  Solve the equation.

The solution set is

16.  Solve the following equation.

$x^{\frac{3}{2}}=64$

 The solution set is

17. Solve the following equation.

$x^{3/5}=–27$

The solution set is

18.  Find the future value and interest earned if ​$8906.54 is invested for 7 years at 5​% compounded ​(a) semiannually and ​(b) continuously.

​(a) The future value when interest is compounded semiannually is approximately _______  (Type an integer or decimal rounded to the nearest hundredth as​ needed.)

The interest earned is approximately ________  ​(Type an integer or decimal rounded to the nearest hundredth as​ needed.)

​(b) The future value when interest is compounded continuously is approximately  _______ ​(Type an integer or decimal rounded to the nearest hundredth as​ needed.)

The interest earned is approximately  _________  (Type an integer or decimal rounded to the nearest hundredth as​ needed.)

19.  Find the present value that will grow to ​$8000 if the annual interest rate is 5.5​% compounded quarterly for 8 yr.

The present value is $ _____

20.   Find the required annual interest rate to the nearest tenth of a percent for ​$1400 to grow to ​$1900 if interest is compounded quarterly for 5 yr.

The required annual interest rate is _______