"Application of Functions" Exponential function and logarithmic function PPT (Application of function model in the third lesson)

Description

"Application of Functions" Exponential function and logarithmic function PPT (Application of function model in the third lesson)

Part One: Learning Objectives

Can use known function models to solve practical problems

Able to establish appropriate function models to solve problems based on actual problems

Application of functions PPT, part 2: independent learning

Problem guide

Preview textbooks P148-P154 and think about the following questions:

1. What are the expression forms of linear and quadratic functions?

2. What are the expression forms of exponential function model and logarithmic function model?

A preliminary exploration of new knowledge

Several common types of function models

self-test

1. The relationship between the reproduction number y (unit: animals) of a certain animal and the time x (unit: years) is y=alog2(x+1). If there are 100 animals of this kind in the first year, by the seventh year they will grow to ()

A． 300 pieces B. 400 pieces

C. 500 pieces D. 600 pieces

2. The output of a certain product this year is a. If the annual growth rate is maintained at 5%, then after x years (x∈N*), the output y of the product satisfies ()

A． y=a(1+5%x) B． y＝a＋5%

C. y＝a(1＋5%)x－1 D. y=a(1+5%)x

3. It is known that the monthly output y of a certain product produced by a factory satisfies the relationship y=a·0.5x+b. It is now known that the factory produced 10,000 pieces and 15,000 pieces of the product in January and February this year, then The factory’s output of this product in March was ________.

Application of functions PPT, the third part: lecture and practice interaction

Application of exponential function model

The original area of ​​a forest is a. It is planned to cut down some trees every year, and the percentage of the area cut down is equal each year. When half of the area is cut down, it will take 10 years. In order to protect the ecological environment, the forest area must retain at least 14% of the original area. , it is known that as of this year, the remaining forest area is 22.

(1) Find the percentage of the area cut down each year;

(2) How many years has the forest been cleared as of this year?

(3) How many more years can it be cut down in the future?

Solving strategy

Solving Strategies for Exponential Function Model Problems

(1) For the growth rate problem, in practical problems, the exponential function model y=N(1+p)x (where N is the basic number, p is the growth rate, and x is time) and the power function model y=a(1+x) can often be used. n (where a is the base number, x is the growth rate, and n is time). When solving problems, logarithmic operations are often used, and attention should be paid to solving the problems corresponding to the values ​​given in the known conditions.

(2) The function y = c·akx (a, c, k are constants) is a widely used function model. It is widely used in electricity, biology, demography, meteorology, etc. to solve such problems. The basic method for solving application problems of the exponential function model is the undetermined coefficient method, that is, determining the relevant coefficients according to the meaning of the problem.

Application of logarithmic function model

Atlantic salmon swim upstream every year and return to their birthplace to spawn. Research has found that the swimming speed of salmon can be expressed as a function v = 12log3θ100, the unit is m/s, and θ is the number of units representing the oxygen consumption of the fish.

(1) When the oxygen consumption of a salmon is 900 units, what is its swimming speed?

(2) If a salmon wants to increase its swimming speed by 1 m/s, then how many times does its oxygen consumption unit increase?

Interactive exploration

(Variable question method) If the conditions in this example remain unchanged:

(1) When the oxygen consumption of a salmon is 8 100 units, what is its swimming speed?

(2) Find the number of units of oxygen consumed by a salmon at rest.

Solving strategy

Basic types and solving strategies of logarithmic function word problems

(1) Basic type: Application questions about logarithmic functions generally give the analytical formula of the function, and then solve it based on actual problems;

(2) Solving strategy: First find the parameters in the analytical formula of the function according to the actual situation, or give a specific situation, extract the data from it, substitute it into the analytical formula for evaluation, and then answer its actual meaning based on the numerical values.

Function word problems with chart information as the background

Function Application PPT, Part 4: Feedback on Compliance

1. The house price (average price) in a certain city increased from 1,200 yuan/m2 to 4,800 yuan/m2 in 6 years. The average annual growth rate during these 6 years is ()

A． 600 yuan B. 50%

C.32-1 D.32+1

2. Under the premise of a fixed voltage difference (voltage is constant), when the current passes through a cylindrical wire, its current intensity I is proportional to the cube of the wire radius r. If it is known that the current passes through a wire with a radius of 4 mm, the current The intensity is 320 A. When the current passes through a wire with a radius of 3 mm, the current intensity is ()

A． 60A B. 240A

C. 75 An D． 135A

3. A company has formulated a reward plan to motivate sales staff: when the sales profit does not exceed 80,000 yuan, 15% of the sales profit will be rewarded; when the sales profit exceeds 80,000 yuan, if it exceeds A million yuan, the excess part will be rewarded at the rate of 15%. Log5(2A+1) is rewarded. Record the bonus as y (unit: 10,000 yuan), and the sales profit as x (unit: 10,000 yuan).

(1) Write the relationship between bonus y and sales profit x;

(2) If salesman Xiao Jiang receives a bonus of 32,000 yuan, how many thousand yuan will his sales profit be?

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For more information about the PPT courseware "Application of Functions, Exponential Functions and Logarithmic Functions, Application of Function Models", please click the Application of Functions ppt Exponential Functions and Logarithmic Functions ppt Application of Function Models ppt tag.

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Update Time: 2024-10-02

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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