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The function f(x)=5000(0.98)^0.3x

represents the number of white-blood cells, per cubic millimeter, in a patient x days after beginning treatment for a virus.

What is the average decrease per day in white-blood cells per cubic millimeter between days 1 and 5?

a.)​ −29.75 mm^3/day
​b.)-34.75 mm^3/day​
c.)-282.47 mm^3/day
d.-)353.08 mm^3/day

Respuesta :

edanielle249
The answer is A.)
f(x)=5000(0.98)^0.3x   What is x=1 and x=5?

f(1)=5000(0.98)^0.3(1)       <<Plug in 1
 = 5000(0.98)^0.3              <<Multiply 1
 =5000(0.993957517)       <<mulitply 0.3 with 0.98
 =4969.78759                    <<mulitply the answer to ^^ with 5000
 =4970                               <<Round


f(5)=5000(0.98)^0.3(5)      <<plug in 5
 = 5000(0.98)^1.5              <<Mulitply 5
 =5000(0.970150504)      <<multiply 1.5 with 0.98
 =4850.75252                   <<muliply the answer to ^^ with 5000
 = 4851                              << round

Next, you do (y2 - y1)/(x2-x1)
 
(4970 - 4851)/(1 - 5)          <<plug in numbers (btw you get the 1 and 5 from                                                                                    plugging them in in the beginning)
=(119)/(4)                               <<Subtract 
 = -29.75                              << divide 

I hope this helps!!
xero099

The average decrease per day in white-blood cells per cubic millimeter between days 1 and 5 is -29.75 cubic millimeters per day. (Correct choice: A)

The average decrease per day in white-blood cells per cubic millimeter is determined by means of the secant line equation, that is to say:

[tex]\dot f = \frac{f(5)-f(1)}{5-1}[/tex]

If we know that [tex]f(x) = 5000\cdot (0.98)^{0.3\cdot x}[/tex], then the average decrease is:

[tex]f(1) = 5000\cdot (0.98)^{0.3\cdot 1}[/tex]

[tex]f(1) \approx 4969.788[/tex]

[tex]f(5) = 5000\cdot (0.98)^{0.3\cdot 5}[/tex]

[tex]f(5) \approx 4850.752[/tex]

[tex]\dot f = \frac{4850.752-4969.788}{5-1}[/tex]

[tex]\dot f = -29.759\,\frac{mm^{3}}{day}[/tex]

The average decrease per day in white-blood cells per cubic millimeter between days 1 and 5 is -29.75 cubic millimeters per day. (Correct choice: A)

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