# Exam review help.

• Jan 22nd 2009, 10:42 AM
Skoz
Exam review help.
1. Solve.

a. 2^x+1=4

2. Simplify. Write each expression using only positive integers.

a. (27x^3y^9)^1/3 b. 3^2/9 x 9^1/3

7. According to the manual, the battery in a cellular phone loses 2% of its charge each day. Assume the battery is 100% charged.
a) Write an equation to represent the percent change, P, as a function of the number of days, x, since the battery was charged.
b) Determine the number of days until the battery is only 50% charged

12. Basket Robin buys its ice cream in cylindrical containers. These containers are approximately 90cm high with a diameter of 36cm. Each scoop has a diameter of 7cm. If each scoop sells for 1.45, how much money is made from ONE container?

18. A skyscraper aways 55cm back and forth from the vertical during high winds. At t=5s, the building is 55cm to the right of the vertical. The building sways back to the vertical and at t=35 s, the building sways 55 cm to the left of the vertical. Write an equation that models the motion of the building in terms of time.
• Jan 22nd 2009, 11:32 AM
earboth
Quote:

Originally Posted by Skoz
1. Solve.

a. 2^x+1=4

2. Simplify. Write each expression using only positive integers.

a. (27x^3y^9)^1/3 b. 3^2/9 x 9^1/3

7. According to the manual, the battery in a cellular phone loses 2% of its charge each day. Assume the battery is 100% charged.
a) Write an equation to represent the percent change, P, as a function of the number of days, x, since the battery was charged.
b) Determine the number of days until the battery is only 50% charged

12. Basket Robin buys its ice cream in cylindrical containers. These containers are approximately 90cm high with a diameter of 36cm. Each scoop has a diameter of 7cm. If each scoop sells for 1.45, how much money is made from ONE container?

18. A skyscraper aways 55cm back and forth from the vertical during high winds. At t=5s, the building is 55cm to the right of the vertical. The building sways back to the vertical and at t=35 s, the building sways 55 cm to the left of the vertical. Write an equation that models the motion of the building in terms of time.

It would have helped me to help you if you have told us where you have difficulties to do those questions.

to #1.a)
I assume that you mean (you should use brackets to make clear which term is the exponent)

$\displaystyle{2^{x+1} = 4~\implies~2 \cdot 2^x=4~\implies~2^x = 2~\implies~2^x=2^1~\implies~x=1}$

to #2.a):

$(27x^3y^9)^{\frac13} = \left(3^3 x^3 y^9\right)^{\frac13}=\left( 3^{3\cdot \frac13} \right)\cdot \left(x^{3\cdot \frac13} \right) \cdot \left(y^{9\cdot \frac13} \right)=3xy^3$

to #2.b):
I assume that you mean:

$3^{\frac29} \cdot 9^{\frac13}=3^{\frac29} \cdot 3^{2 \cdot \frac13}=3^{\frac29+\frac23} = 3^{\frac89}$

to #7:

Let x denote the time measured in days. Then

$P(x)=100 \cdot (0.98)^x$

$P(x)=50~\implies~50=100\cdot (0.98)^x~\implies~\dfrac12=(0.98)^x~\implies~x=\lo g_{0.98}\left(\frac12\right)$
Use the base change formula to calculate an approximate value of x:

$x = \dfrac{\ln\left(\frac12\right)}{\ln(0.98)}\approx 34.3\ days$

I haven't enough time to do the last two questions.