Answer:
- P(t) = 100·2.3^t
- 529 after 2 hours
- 441 per hour, rate of growth at 2 hours
- 5.5 hours to reach 10,000
Step-by-step explanation:
It often works well to write an exponential expression as ...
value = (initial value)×(growth factor)^(t/(growth period))
(a) Here, the growth factor for the bacteria is given as 230/100 = 2.3 in a period of 1 hour. The initial number is 100, so we can write the pupulation function as ...
P(t) = 100·2.3^t
__
(b) P(2) = 100·2.3^2 = 529 . . . number after 2 hours
__
(c) P'(t) = ln(2.3)P(t) ≈ 83.2909·2.3^t
P'(2) = 83.2909·2.3^2 ≈ 441 . . . bacteria per hour
__
(d) We want to find t such that ...
P(t) = 10000
100·2.3^t = 10000 . . . substitute for P(t)
2.3^t = 100 . . . . . . . . divide by 100
t·log(2.3) = log(100)
t = 2/log(2.3) ≈ 5.5 . . . hours until the population reaches 10,000
C - 0.17c = 0.83c
When you write “c” at the start, or x or whatever, it has an understood (invisible) number 1. So you’re subtracting the decimal on the next variable from 1.
<u>Answer:</u>
Below!
<u>Explanation:</u>
Exponents are small numbers that defines how many times does the base needs to multiply itself. Two exponents can also be classified in words. 'Squared' defines a number multiplying itself two times. 'Cubed' defines a number multiplying itself three times. If there is a zero as the base's exponent, this means that the result will always be 1. Now, let's solve all the problems together.
- 2¹ = 2
- 3⁵ = 3 x 3 x 3 x 3 x 3 = 243
- 4³ = 4 x 4 x 4 = 64
- 6⁴ = 6 x 6 x 6 x 6 = 1256
- 7⁴ = 7 x 7 x 7 x 7 = 2401
- 1⁶ = 1 x 1 x 1 x 1 x 1 x 1 = 1
- 8² = 8 x 8 = 64
- 2³ = 2 x 2 x 2 = 8
- 4⁴ = 4 x 4 x 4 x 4 = 256
- 10³ = 10 x 10 x 10 = 1000
- 12² = 12 x 12 = 144
- 5⁴ = 5 x 5 x 5 x 5 = 625
- 6² = 6 x 6 = 36
- 3⁶ = 3 x 3 x 3 x 3 x 3 x 3 = 729
- 7³ = 7 x 7 x 7 = 343
- 2⁴ = 2 x 2 x 2 x 2 = 16
- 11⁰ = 1
- 4³ = 4 x 4 x 4 = 64
- 1¹² = 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 1
Hoped this helped!
Answer:
219 employees
Step-by-step explanation:
3% of decreasing rate of employees per year is calculated thus:
In 9 years,
Therefore, the number of employees for a certain company where decreasing rate of employees is 3% and continued to decrease for 9 years; and 810 employees are currently working is 219 employees. By implication, 810 + 219 = 1029 employees were working in the company 9 years ago.
Answer: 18/7
Step-by-step explanation: random.
