Each of the functions listed below gives the amount of a substance present at ti

Question

Each of the functions listed below gives the amount of a substance present at time t. In each case give the amount present initially (at t = 0), state whether the function represents exponential growth or decay and give the percent growth or decay rate. A = 300(1.04)^4 Initial Amount: Circle One: Growth Decay Rate: A = 30(1.4) Initial Amount: Circle One: Growth Decay Rate: A = 3000(0.96) Initial Amount: Circle One: Growth Decay Rate: (Include % sign) Mathberg is a town with a population of 4200 time t = 0. In each of the following cases, write a formula for the population, P, of Mathberg as a function of the year t. The population increases by 192 people a year: The population increases by 4% per year: If you use your function from part a, what will the population be in 15 years? If you use your function from part b, what will the population be in 15 years? P is an exponential function of time: P = P_0 a^t If we know P_0 a^4 = 18 & P_0 a^3 = 20 Find a & P_0 Give P_0 rounded to 3 decimal places: P_0 = Give the exact value for a: a = Based on our value of a, what type of exponential function do we have? Growth Decay Find a possible formula for the function represented by the data in the table. Use proper function notation. The company that produces Cliff Notes (abridged versions of classic literature) was started in 1958 with $4,000 and sold in 1998 for $14,000,000. Find the annual percent increase (round o the nearest tenth of a percent) in the value of this company, over the 40 years. The value of the company increased at an average rate of per year. (Your answer should have a percent size)

Explanation / Answer

26. a A=300(1.04)t

Wer have to compare it with

A= a (1+r)t

And we can write the above expression as

A=300(1+.04)t

So its growth function where rate is 4%

b. A=30(1.4)t

A=30(1+.4)t

So its growth function where rate is 40%

c. A=3000(0.96)t

A=3000(1-.04)t

So its decay function and rate is 4%

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