5. You put $7,500 into a bank account that has a very high continuously compounded interest rate of 18%. Assuming that no money is withdrawn, how many years will you have to wait before you have enough money to pay for a $42,000 car? 1.887 years O 9.571 years 9.572 years 10.413 years 11.414 years 6. Solve for y(t) if the following adheres to the exponential growth/decay model. y(0)=32 and the rate of growth is 2.8% O y(t) = 320.028: O y(t) = 0.028e12t O y(t) = Kel.026+32 O y(t) = 0.028e32 O y(t) = 320.026x 7. The half-life of a 1000 gram substance is 50 years. If it decays according to an exponential growth model, the amount of time it will take for the substance to be only 100 g is Between 150 and 155 years Between 165 and 170 years O Between 160 and 165 years O Between 155 and 160 years 8. A city believes its maximum population capacity to be 300,000. If the city currently has 100,000 people, and the population grows 3% every year, how long will it be until the city reaches their capacity? O 53.173 years 69.322 years O 19.123 years O 8.651 years 36.620 years1. For the function f, fi(x) = -2: +1 and / (-2) = -4. Find the approximation for f (-1.6) by using the line tangent to the graph of f at * = -2. O -12 O -6.56 -5 O -2 O -2.16 2. Using the line tangent to the curve f (x) = sin(x) at = = 3, what is the local linear approximation for sin(1)? Notice that, since { = is close to 1, we should be able to get a good linear approximation for sin(1). O sin(1) 143V3 x O sin(1) = 1-vita O sin(1) # 1tyl 2 O sin(1) 1tavl O sin(1) 1373 avi 3. For the function f, f/(x) = 6: -7 and f (1) = 0. Find the approximation for f (1.1) by using the line tangent to the graph of f at = = 1. 0.12 O -0.1 0.06 O -0.07 4. What formula would be used to calculate a local linear approximation for f (x) = 1 around a = 1? Ov=z-1 Oy=-2+1 Oy= -1(2-1) Oy=1 Oy=-x+2 5. Using the line tangent to the curve f (x) = =' - 2: + 1 at 2 = -2, what is the local linear approximation for f (-1.8)? O -1.2 -2 -3 O -2.1 O -11. The rate at which the density of weeds in a certain field is increasing at any given time, t, is directly proportional to the density of weeds at that time. If the original density of the weeds in the field is 5 weeds per square meter, and after 2 months (t = 2), the density of weeds is 8.75 weeds per square meter, which of the following functions best represents the density of the weeds at time t? O y = 8.75elm(1.75) Oy = 5(1.75)# O y = 5e(1.75)4 Oy = }In(1.75)est Oy= 5(} In(1.75))' 2. The rate at which a certain bacteria population grows is modeled by the equation # = ky. If y = 123 when t = 1 and y = 357 when t =3, what is the rate of growth of the bacteria population? In(112 ) 123 V W O 357 In( ") O In( 18 ) 3. The rate of growth of a lizard population in a small area of the Mojave desert is proportional to the amount of lizards already in the population. If the population grows continually at a rate of 11%, and there are originally 250 lizards in the population, how many months does it take for the lizard population to triple? 2.938 months 5.638 months 10.532 months 9.987 months 1.104 months 4. Find the exponential growth model that satisfies a = ky, grows at 6% per year, and has the initial condition y(0) = 2. O y = 2e 1.084 O y = 2e-0.08e Oy=e-0.064 +1 Oy =0.Dot - 2 Oy = 0.Dot + 16. Using the line tangent to the curve f (x) = a* - 2 at : = 1, what is the local linear approximation for f (1.3)? O -0.6 0.22 1.6 O -0.31 O -0.4 7. What is the formula of the line tangent to the curve f (x) = 2Va at * = 47 Ov= =+2 Oy= -4+1 Oy=2va -4 Oy=4 Oy= 1(x-4) Calcul 8. (% error) = factual vala) (approximated vala) | x 100%% (actual value) Use the formula above to find the answer to the following question: For the function f, f/(x) = sin(@) + r and f (1) = 2. For the approximation of f (0.9), found by using the line tangent to the graph of f at a = 1, the % error of the approximation is O between 0% and 1%. O between 1% and 2%. O between 2% and 3%. O between 3% and 4%. O greater than 4%. 9. (% error) = factual valo) (approximated value) | X 100%% (actual value) Use the formula above to find the answer to the following question: If the local linear approximation of f (2:) = 3 sina + els at x-2 is used to find the approximation for f (1.9), then the % error of this approximation is... O Between 2% and 4% O Between 4% and 6% Between 6% and 8% O Between 8% and 10% O Greater than 10%Which of the following alope fields describes the differential equations - O 5. The skype feld for a specific differential equation is shown below. -3 Which of the following could be a solution to the differential equation with an initial condition of p[1] - 1? Oy-1-2 2-1-1 O # =2v2 -1-1 Oy-+ +1 Oy-1- 5. For the differential expiation # = Time what is the slope of y at (0, #)? 011.If = -, what is the slope of y at the point (3, -1)? O -3 O 3 O It cannot be determined from the given information. 2. For the differential equation what is the slope of y at (0, 2)? O2 O 1 O 1 3. Which of the following slope fields describes the differential equation { = x sin(y)? -3- 4 -3 -2 -1 0 1 2 3 -543 2 1 0 2 5