Chapter 8: Exponents and Exponential Functions.

Scientific notation

100

IS THIS SCIENTIFIC NOTATION: 0.09394058305860385058603485068X10^90

NO IT NOT. BECAUSE: IT UNDER 1. I WIN.

200

Write down a Googolplex in scientific notation

If you put down 10^Googol then your correct SIKE THATS A INVALID ANSWER Valid: 10^10^100

300

(5 x 10^6) (2x 10^3) (3x 10^3) _________________________ = ??? 5 x 10^4

6X10^8

400

(4 x 10^6) (5x 10^-3) ___________________ = (8 x 10 ^-4 )(5x 10^3)

5X10^3

500

The speed of light is 3 x 10 8 meters/second. If the sun is 1.5x 1011 meters from earth, how many seconds does it take light to reach the earth. Express your answer in scientific notation

5.0X10^2

Exponents

100

1039485035584573406430963406.20438583205835676320576032867230236760375958^0 is equal too?

1

200

10a^-6

1/10a^6

300

Evaluate 3m^2*T^-2 for M=2 and T=-3 SIMPLIFY IT

1 1/3

400

Simplify: c^5(c^3)c^-2

1/C

500

Simplify (x^-2)^2(3xy^2)^4

81y^8

Geometric Sequence

100

Find the common Ratio 80, 20, 5, 5/4

The common Ratio is 1/4

200

Arithmetic or Geometric? 56, 28, 14, 7, 3 1/2, 1.75

Geometric * 1/2

300

Find the 10 th term of a geometric sequence if a1 = 45 and the common ration r = 0.2. (hint:Use the formula A(n) = A(1) * r^N-1)

a10 = a1 * rn-1 = 45 * 0.29 = 2.304 * 10-5

400

Find the next three terms of the geometric sequence. 243, –81, 27, .....

The next 3 terms are –9, 3, and –1.

500

Arithmetic or Geometric 55, 51, 47, 43, 39, 35, . . .

Trick Question Neither

Exponential Functions

100

Y=5^x x= 2, 3, 4

25, 125, 625

200

Suppose 20 rabbits are taken to an island. The rabbit population then triples ever half- year. the function f(x)= 20*3^x, where x is the number of half- year periods, model this situation. how many rabbits would there be after 4 years?

131220

300

Which function contains the points (1,3) and (3, 6.75) (a): 1.675x+1.325 (b): 1.5*2^x (c): 1.325x+1.675 (d):2*1.5^x

(D)

400

Which function is greater at the given value: f(x)=2^x or f(x)= 100x^2 at x=10

F(x)=100x^2

500

Suppose an investment of $2000 dollars doubles in value every 8 years. how much is the investment worth after 24 years? after 32 years?

16,000 32,000

Over-complicated problems

100

The population in the town of Huntersville is presently 38,300. The town grows at an annual rate of 1.2%. Find the number of years it takes for the population to grow to 42,500.

approximately 9 years

200

Max decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account?

Approximately 17.4 years

300

You tell victor a secret. Victor see no harm in telling two friends. After this second "passing" of the secret, 4 people now know the secret ( you, Victor and two friends). If each of these friends now tells two new people, after the third "passing" of the secret, eight people will know. If this pattern of spreading the secret continues, how many people will know the secret after 10 such "passings"?

The number of people "knowing" the secret grows in an exponential pattern, with the number of people doubling after each pass of the secret. 1, 2, 4, 8, ..... 21 , 22 , 23 , ..... Equation: y = 2x where x is the number of the "pass". Answer: 210 = 1024 people.

400

The number of wolves in the wild in the northern section of the Cataragas county is decreasing at the rate of 3.5% per year. Your environmental studies class as counted 80 wolves in the area. After how many years will this population of 80 wolves drop below 15 wolves, if this rate of decrease continues? round to the nearest whole number

x= 46.98, 47

500

The mass of Mercury is about 3.302 x 10^20 metric tons. The mass of the sun is about 1.998 x 10^27 metric tons. About how many times the mass or Mercury is the mass of the sun? Give your answer in Scientific Notation. (Round to the nearest thousandth as needed. Use Scientific Notation.)

The mass of Mercury = 3.302 x 10^20 metric tons. The mass of the sun = 1.998 x 10^27 metric tons. How many times the mass of Mercury is the mass of the sun? = ( 1.998 x 10^27 ) / ( 3.302 x 10^20 ) = ( 1.998 / 3.302) *( 10^27 / 10^20 ) = 0.605 * 10^7 = 6.05 * 10^6 times Or, we can do it this way. 1.998 x 10^27 -------------------- = 3.302 x 10^20 1.998 ---------- x 10^7 = 0.6050878 x 10^7 3.302 = 6050878 times or 6.051 * 10^6 times