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)
Answer:
y = x - 10
Step-by-step explanation:
Answer:
x=1
Step-by-step explanation:
slope AB = (7-5) / (3 - -1) = 2 / 4 = 1/2
slope CD = (23-11) / (x-7) = 12 / (x-7)
12 / (x-7) = - 2 ... perpendicular to AB slope 1 = - 1/slope 2
-2 (x-7) = 12
-2x + 14 = 12
-2x = -2
x = 1
Answer:
Step-by-step explanation:
<u>Exponential function is:</u>
<u>Use two points on the graph to determine the value of a and b:</u>
<u>Find the values of a and b:</u>
- f(0) = a*b⁰ = a = 100
- f(1) = a*b¹ = ab = 100b = 50 ⇒ b = 50/100 = 1/2
<u>The function is:</u>
x first so five to the left so it's negative and if each gridline is .5 and were are 5 gridlines aver then .5*5 so -2.5 then y is up so positive and 3 lines so .5*3 so 1.5 so coordinate is (-2.5,1.5)
