math homework . need to be doe. it wont take you time…………………………

Written Assignment #2: Exponential and Logarithmic Functions: Graphing and

Applications

Instructions: This assignment is to be completed and submitted ONLINE on or before APRIL 13th.

Use the BOXES provided to show all of your work, and make your graphs clear and neat. Points will

be deducted if your graphs are unnecessarily small or difficult to read.

Problem 1. Let 𝑓(𝑥) = 2𝑥 , and let 𝑔(𝑥) = log 2 𝑥. Complete tables, then, graph BOTH functions on the same set

of axes.

7 𝑥

Problem 2. Let 𝑓(𝑥) = (4) , and let 𝑔(𝑥) = log 7/4 𝑥. Complete tables, then, graph BOTH functions on the same

set of axes.

2 𝑥

Problem 3. Let 𝑓(𝑥) = (5) . Complete table and graph the function 𝑓(𝑥).

Problem 4. The amount of electricity that a solar panel is capable of producing slowly decays over time. After ten

years, a solar panel produces 89% of the electricity that it was able to produce when it was brand new. Find the

exponential decay constant k. If a solar panel is initially capable of producing 450 watts of power, how long will it

take before the solar panel is only able to produce 300 watts of power?

Problem 5. Suppose you invest $3,000 at an interest rate of %6.

a)

b)

c)

d)

If the interest is compounded semiannually, how much money will you have after 15 years?

If the interest is compounded semiannually, how long will it take for you to have $14,000?

If the interest is compounded continuously, how much money will you have after 15 years?

If the interest is compounded continuously, how long will it take for you to have $14,000?

Problem 6. The total number of electric cars that are sold each year has been growing exponentially. In the initial

year of major production (year zero), 50,000 electric cars were sold world wide. Four years later, the number of

cars sold in a year had increased to 500,000. Find the exponential growth constant k and write down an

exponential function A(t) that models the number of electric cars sold in year t of major production. According to

this model, how many cars will be sold in year ten? How many years (after the initial year of major production)

will pass before the number of electric cars sold in a year reaches 100,000,000?

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