HELP!

Mathematics

1 answer:

Leni [432]3 years ago

7 0

He drove 14 miles per gallon.

Step-by-step explanation:

Total distance = 278.2 miles

Gasoline used = 19.6 gallons

We need to find the unit rate of gallon, therefore, we will divide the total distance covered with the gasoline used to find the distance drove with 1 gallon of gasoline.

Distance per gallon = $\frac{Total\ distance}{Gasoline used}$

Distance per gallon = $\frac{278.2}{19.6}\\$

Distance per gallon = $14.19\ miles$

Rounding of to nearest whole amount;

Distance per gallon = 14 miles

He drove 14 miles per gallon.

Keywords: distance, unit rate

Learn more about distances at:

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A quantity P is an exponential function of time I, such that P = 160 when t = 6 and P = 150 when I = 4. Use the given informatio

Klio2033 [76]

Answer:

k = 0.032
P0 = 131.836

Step-by-step explanation:

Perhaps you want to use the points (t, P) = (4, 150) and (6, 160) to find the parameters P0 and k in the equation ...

$P(t)=P_0\cdot e^{kt}$

We know from the given points that we can write the equation as ...

$P(t)=150\left(\dfrac{160}{150}\right)^{(t-4)/(6-4)}=150\left(\dfrac{16}{15}\right)^{\frac{t}{2}-2}\\\\=150\left(\dfrac{16}{15}\right)^{-2}\times\left(\left(\dfrac{16}{15}\right)^{\frac{1}{2}}\right)^t$

Comparing this to the desired form, we see that ...

$P_0=150\left(\dfrac{16}{15}\right)^{-2}\approx 131.836\\\\e^{k}=\left(\dfrac{16}{15}\right)^{1/2}\rightarrow k=\dfrac{1}{2}(\ln{16}-\ln{15})\approx 0.0322693$