Suppose the amount of bacteria growing in a perti dish is represented by the function b(t)=50t/t+1

Evaluate the function at t=1,2,5,10,15,20 (a) constract a table of values (b) use the table to sketch a graph.

To evaluate the function at the given values of t, we substitute each value into the function b(t) = 50t/(t+1).

(a) Table of values:

t | b(t)
---------
1 | 50/2 = 25
2 | 100/3 ≈ 33.33
5 | 250/6 ≈ 41.67
10 | 500/11 ≈ 45.45
15 | 750/16 ≈ 46.88
20 | 1000/21 ≈ 47.62

(b) To sketch the graph, we plot the values from the table as points on a coordinate grid using t as the x-coordinate and b(t) as the y-coordinate.

The graph will start near zero when t is close to 0 and approach 50 as t increases.

Here is a rough sketch of the graph:

|
50 | X
| X
| X
| X
| X
| X
|
------------------
0 5 10 15 20

To evaluate the function at different values of t, we can substitute the given values of t into the function b(t)=50t/t+1 and simplify the expression.

(a) Constructing a table of values:
We will substitute the values t=1, 2, 5, 10, 15, and 20 into the function b(t)=50t/t+1.

For t=1:
b(1) = 50(1)/(1+1) = 50/2 = 25

For t=2:
b(2) = 50(2)/(2+1) = 100/3 ≈ 33.33

For t=5:
b(5) = 50(5)/(5+1) = 250/6 ≈ 41.67

For t=10:
b(10) = 50(10)/(10+1) = 500/11 ≈ 45.45

For t=15:
b(15) = 50(15)/(15+1) = 750/16 ≈ 46.88

For t=20:
b(20) = 50(20)/(20+1) = 1000/21 ≈ 47.62

Here is the resulting table of values:

t | b(t)
-------------
1 | 25
2 | 33.33
5 | 41.67
10 | 45.45
15 | 46.88
20 | 47.62

(b) Sketching the graph:
To sketch the graph, we can plot the values from the table on a graph, using the values of t as the x-coordinates and the corresponding values of b(t) as the y-coordinates.

The graph will show the relationship between t (the time) and b(t) (the amount of bacteria). The y-axis represents the amount of bacteria (b(t)), while the x-axis represents time (t). Connect the plotted points with a smooth curve to get an approximate shape of the graph.

Note: Since we only have a few specific points, it may not accurately represent the shape of the entire graph, but it will give us a general idea.

Here is a rough sketch of the graph:

|
| * (20, 47.62)
|
| * (15, 46.88)
|
|
b(t)|---------* (10, 45.45)
|
|
|
| * (5, 41.67)
|
|
|
| * (2, 33.33)
|
|
| * (1, 25)
|
---------------------------------
1 5 10 15 20 t

Please note that the graph is just an approximation based on the given points. The actual shape and behavior of the graph may vary.

no answer

Surely you meant:

b(t) = 50t/(t+1) or else the t's would just cancel

b(1) = 50(1)/(1+1) = 51/2 or 25.5
b(2) = 50(2)/(2+1) = 100/3 = ...
b(5) = 50(5)/(5+1) = 250/6 = ..
etc