Laboratory technicians recorded the population of a species of bacteria each hour for 7 hours. The population in
thousands after x hours can be modeled by the exponential function f(x) = 575(1+040).
Choose the correct answer from each drop-down menu to complete the statements.
The initial population of bacteria when the technicians began recording was BLANK 1.
The population is BLANK 2 at the rate of BLANK 3 per hour.
BLANK 1 ?
805,000
575,000
230,000
BLANK 2 ?
805,000
575,000
230,000
BLANK 3
805,000
575,000
230,000
The initial population of bacteria when the technicians began recording was 575,000.
The population is increasing at the rate of 40,000 per hour.
can you explain your work
Sure!
In the given exponential function, f(x) = 575(1+0.40x), the initial population is given by the coefficient of the function, which is 575. This means that when x=0 (when the technicians began recording), the population was 575,000 (575 multiplied by 1,000, because the function is given in thousands).
To determine the rate at which the population is increasing per hour, we look at the coefficient of x in the function, which is 0.40. This means that for every hour that passes (for each increment of x), the population increases by 0.40 multiplied by the initial population.
In this case, 0.40 multiplied by 575,000 (the initial population in thousands) gives us 230,000. This means that the population is increasing at a rate of 230,000 per hour.
So the final answers are:
The initial population of bacteria when the technicians began recording was 575,000.
The population is increasing at a rate of 230,000 per hour.
if you were just solving this can yopu show me your numbner work
Certainly! Here is the step-by-step calculation:
Given function: f(x) = 575(1+0.40x)
1. Initial population when x=0:
f(0) = 575(1+0.40(0))
= 575(1+0)
= 575(1)
= 575,000
2. Rate of population increase per hour:
The coefficient of x is 0.40, which means that for every hour, the population increases by 0.40 times the initial population.
Rate = 0.40 * 575,000
= 230,000
So, the initial population was 575,000 and the population is increasing at a rate of 230,000 per hour.
what about the secound blank
I apologize for the confusion. The second blank should be filled with the value of f(x) at the given value of x. In this case, the population after x hours can be calculated by plugging in the value of x into the function.
Since we are given that x=7, we can calculate f(7):
f(7) = 575(1+0.40(7))
= 575(1+2.8)
= 575(3.8)
= 2,185,000
So, the population after 7 hours is 2,185,000 (2.185 million).
Therefore, the correct answer for the second blank is 2,185,000.
thyat is incorrect
Apologies for the mistake. Let's calculate the correct value for the second blank using the given exponential function:
f(x) = 575(1+0.40x)
To find the population after 7 hours (x = 7), we substitute x = 7 into the function:
f(7) = 575(1+0.40(7))
= 575(1+2.8)
= 575(3.8)
= 2,185
Therefore, the correct answer for the second blank is 2,185.