3. Steve is on a road trip and notices that the gas left in his tank is decreasing at a constant rate. He determines that the amount of gas left in his tank can be given by the function\( G = - \frac { 1 } { 25 } m + 16 \) , where \( m \) is the number of miles that Steve has driven.
a. Identify the vertical intercept, and interpret its meaning in the context of this problem.
b. Identify the slope, and interpret its meaning in the context of this problem.
3.
a. 16. This is the initial fuel in the tank before Steve has driven the vehicle.
b. -1/25. The slope has the units of amount of gas per mile. Thus, it measures how much fuel is used per driven mile. The negative sign is there to show that the fuel in the tank is indeed decreasing.
Find the solution of the exponential equation \( 16 e ^ { x } = 12 \) in terms of logarithms, or correct to four decimal places. \( x = \)
Certain radioactive material decays in such a way that the mass remaining after \( t \) years is given by the function
\( m ( t ) = 100 e ^ { - 0.01 t } \)
where \( m ( t ) \) is measured in grams. (a) Find the mass at time \( t = 0 \) . Your answer is (b) How much of the mass remains after \( 20 \) years? Your answer is Round answers to \( 1 \) decimal place.
