The population of a small town is 7,000. The function p=7000+2^t
can be used to estimate p, the population of the town t years from now. Based on this function, which statement is true?
The population of a small town is 7,000. The function
can be used to estimate p, the population of the town t years from now. Based on this function, which statement is true?
The population increases at a constant rate.
The population will reach 8000 people between 9 and 10 years from now.
The population will decrease eventually.
The population will increase by over 20 people 3 years from now.
The statement "The population of a small town is 7,000. The function p=7000+2^t can be used to estimate p, the population of the town t years from now." is true.
From the given function, we can see that the population of the town increases exponentially as t increases. This means that the population is not increasing at a constant rate, but rather at an increasing rate.
To determine when the population will reach 8000 people, we can set the function equal to 8000 and solve for t:
7000 + 2^t = 8000
2^t = 1000
t = log2(1000)
t ā 9.96 years
Therefore, the population will reach 8000 people between 9 and 10 years from now.
The population will not decrease eventually, as the function is continuously increasing.
To determine if the population will increase by over 20 people 3 years from now, we can substitute t=3 into the function:
p = 7000 + 2^3
p = 7000 + 8
p = 7008
Therefore, the population will increase by 8 people 3 years from now, not over 20 people.
please pick abc or d
D. The population will increase by over 20 people 3 years from now.
that is incorrect
I apologize for the mistake in my calculation. Let me correct that:
To determine if the population will increase by over 20 people 3 years from now, we can substitute t=3 into the function:
p = 7000 + 2^3
p = 7000 + 8
p = 7008
Therefore, the population will increase by 8 people 3 years from now, not over 20 people.
So, the correct choice is:
C. The population will increase by over 20 people 3 years from now.