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In this lesson, we will learn how to find the intersection of an exponential function with the coordinate axes.

Q1:

What is the point of intersection of the π¦ -axis and the graph of the function π ( π₯ ) = 9 ο ο° ο§ ?

Q2:

The population of a country was 22 million people at the end of 2010. Since then, the population has increased by 1 . 8 % yearly. Determine the population of the country at the end of 2023. Give your answer in units of millions, correct to two decimal places.

Q3:

The curve with equation is the image of the curve with equation under reflection in which axis?

Q4:

Determine whether the function is increasing or decreasing.

Q5:

Find the domain and range of π ( π₯ ) = οΌ 1 8 ο π₯ , and determine whether it is an increasing function or a decreasing function.

Q6:

Find the domain and range of π ( π₯ ) = 8 π₯ β 2 , and determine whether it is an increasing function or a decreasing function.

Q7:

For what values of π is the function π ( π₯ ) = π π₯ increasing on its domain?

Q8:

Consider an exponential function with base π . For which values of π is the function decreasing?

Q9:

The graph shows the two functions π ( π‘ ) = 1 0 οΉ 0 . 9 4 ο ο and π ( π‘ ) = 1 5 οΉ 0 . 9 4 ο ο defined for π‘ β₯ 0 . Both are decaying at a rate of 6 % .

What is the ratio of π ( 1 2 ) π ( 1 2 ) ?

What is the ratio of π ( 4 2 ) π ( 4 2 ) ?

Suppose that π ( π‘ ) = 1 0 π ο and π ( π‘ ) = 1 5 π ο with π , π > 0 . How do π and π compare if π ( π ) = π ( π ) at some point π ?

Q10:

Suppose that π ( π₯ ) = 0 . 3 ( 4 ) ο .

Evaluate π ( 0 ) .

Evaluate π ( 2 ) .

Evaluate π ( 0 . 5 ) .

Evaluate π οΌ β 1 2 ο .

Q11:

Find the point of intersection of the graph of π ( π₯ ) = 2 π₯ with the straight line π¦ = 1 6 .

Q12:

What is the point of intersection of the π¦ -axis and the graph of the function π ( π₯ ) = 9 ο¨ ο± ο ?

Q13:

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