The population of rabbits is modeled by the exponential function
where R(t) is the population at time t in years.
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Question 1
1.
What is the initial population of the rabbits in this model?
_______ rabbits
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Question 2
2.
Does this model growth or decay?
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Question 3
3.
Determine the annual growth rate of the rabbit's population.
_______ %
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Question 4
4.
Rounding to the nearest rabbit, how many rabbits will there be after 3 years?
About _______ rabbits.
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Question 5
5.
How long do you think it will take for the rabbit population to double from the initial amount?
Justify your answer.
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Question 6
6.
A town has a population of 12000 and grows at 3.5% every year.
What will be the population after 7 years, to the nearest whole number?
About _______ people.
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Question 7
7.
A new car is purchased for 16400 dollars. The value of the car depreciates at 12.5% per year. What will the value of the car be, to the nearest cent, after 8 years?
$_______
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Question 8
8.
Try setting this up as an equation to solve.
9700 dollars is placed in an account with an annual interest rate of 6.25%.
How long will it take for the account value to reach 51700 dollars?
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Question 9
9.
Try setting this up as an equation to solve.
An element with a mass of 300 grams decays by 5.4% per minute.
How long will it be until there are 110 grams of the element remaining?
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Question 10
10.
Write the exponential equation as a logarithmic equation.
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Question 11
11.
Write the exponential equation as a logarithmic equation.
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Question 12
12.
Write the logarithmic equation as an exponential equation.
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Question 13
13.
Write the logarithmic equation as an exponential equation.
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Question 14
14.
Evaluate the value of
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Question 15
15.
Evaluate the value of
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Question 16
16.
Evaluate the value of
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Question 17
17.
Evaluate the value of
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Question 18
18.
Evaluate the value of
No base means base 10, calculator ready.
Using Log to Solve an Exponent
Example:
A town has a population of 10000 and grows at 5% every year.
To the nearest year, how long will it be until the population will reach 22000?
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Question 19
19.
You Try!
4500 dollars is placed in an account with an annual interest rate of 7%. To the nearest tenth of a year, how long will it take for the account value to reach 10800 dollars?