State the equation of the horizontal asymptote

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Assignment Questions -

Q1. Simplify the following. Express each answer with positive exponents.

a. (w⁴(w^-3))/(w^-2)^-1

b. √(25m^-12)/√(36m¹⁰)

c. (((x³y)^-1(x⁴y³))/(x²y^-3)^-2)^-1

Q2. An insect colony, with an initial population of 20, quadruples every day.

a. Complete the table.

Day	Population	First Differences	Second Differences
0	20
1	80
2
3
4
5

b. Write an equation of the form y = a ⋅ b^x to model the data.

c. Graph the data.

d. Is this an example of exponential growth or decay? Explain your answer.

Q3. Solve the following exponential equations.

a. 3^x+4 = 27

b. 5^4x+2 = 25^x-1

c. 6^3x-7 = 1/6

d. 2^x+2 - 2^x = 48

Q4. For the function f(x) = -3 ⋅ 2^x-1 - 5:

a. State the equation of the horizontal asymptote.

b. State the mapping rule for the transformed function.

c. Sketch a graph of the transformed function.

d. State the domain and range of the transformed function.

Q5. Tungsten-187 is a radioactive isotope that has a half-life of 1 day. Suppose you start with a 100-mg sample. How much is left after 5 days?

Q6. The half-life of carbon-14 is 5730 years. How long does it take for a 120 gram sample to decay to 1.875 grams?

Reference no: EM132303073

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