To find: a) The speed of the sprinter while he running

preprekomW

preprekomW

Answered question

2021-08-18

To find:
a) The speed of the sprinter while he running as crossed the finish line
b) After how many seconds was he running at the rate of 10 m per sec
Using the model function f(t)=11.65(1et1.27) where f(t) is the speed of the sprinter per second after t seconds.

Answer & Explanation

mhalmantus

mhalmantus

Skilled2021-08-19Added 105 answers

Concept:
Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.
Calculation:
The given model function is f(t)=11.65(1et1.27)
where f(t) is the speed of the sprinter per second after t seconds.
a) The sprinter finished the race in 9.86 seconds.
So, substituting x=9.86, we het the speed of the sprinter while he crossing the finish line.
Let x=9.86,f(9.86)=11.65(1e9.861.27)
Using the calculator, f(9.86)=11.65×(10.00042484781)
f(9.86)=11.65 meters per second if rounded to nearest hundredth.
The speed of the sprinter while he running as crossed the finish line is 11.645 m/sec.
b) The speed of the sprinter is given by 10 m/sec.
So, f(t)=10
So, f(t)=11.65(1et1.27)=10
Divide each side by 11.65, (1et1.27)=1011.65
Using calculator, (1et1.27)=0.858369
10.858369=et1.27
et1.27=0.1416
Taking natural logarithm on each side, In (et1.27)=In0.1416
Using calculator, (t1.27)logee=loge0.1416
t1.27=1.9547
Divide by 1,t1.27=1.9547
Using calculator, t=1.9547×1.27
Rounded to nearest hundredth, t2.48 seconds.
So, after 2.48 seconds his speed was 10 m/sec.
Final statement:
a) The speed of the sprinter while he running as crossed the finish line is 11.65 m/sec.
b) After 2.48 seconds was he running at the rate of 10 m per sec.

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