Complete question:
The growth of a city is described by the population function p(t) = P0e^kt where P0 is the initial population of the city, t is the time in years, and k is a constant. If the population of the city atis 19,000 and the population of the city atis 23,000, which is the nearest approximation to the population of the city at
Answer:
27,800
Step-by-step explanation:
We need to obtain the initial population(P0) and constant value (k)
Population function : p(t) = P0e^kt
At t = 0, population = 19,000
19,000 = P0e^(k*0)
19,000 = P0 * e^0
19000 = P0 * 1
19000 = P0
Hence, initial population = 19,000
At t = 3; population = 23,000
23,000 = 19000e^(k*3)
23000 = 19000 * e^3k
e^3k = 23000/ 19000
e^3k = 1.2105263
Take the ln
3k = ln(1.2105263)
k = 0.1910552 / 3
k = 0.0636850
At t = 6
p(t) = P0e^kt
p(6) = 19000 * e^(0.0636850 * 6)
P(6) = 19000 * e^0.3821104
P(6) = 19000 * 1.4653739
P(6) = 27842.104
27,800 ( nearest whole number)
The LCM is 540 because 54X10=540 which 20 goes into
Answer:
5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4
Step-by-step explanation:
The Associative Property is applied to two types of operations: addition and multiplication. This property indicates that, when there are three or more terms in these operations, the result does not depend on the way in which the terms are grouped.
In this sense, the associative property for the sum is mathematically given by:
and for the multiplication by:
Now, let:
Using the Associative Property of Multiplication:
Therefore the equivalent expressions are:
5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4
