MAT1630_S20_e1_v2_sol.ipynb

Kernel: Python 3 (Anaconda 2019)

Exam 1 v2 Solutions

Problem 1

a)

b)

def minBusCost(m,n):
    cost = 24*m + 34*n
    if cost < 1300:
        return cost
    else:
        return 1300

Problem 2

a)

for x in range(51):
    for y in range(51):
        if 86*x-25*y == 16:
            print(x,y)

6 20

b)

[2*n for n in range(1,1567) if 1566%(2*n)==0]

[2, 6, 18, 54, 58, 174, 522, 1566]

Problem 3

a)

1200*(1+0.036/12)**(12*12)

1847.2071502050508

b)

-(4000-1200*(1+0.036/12)**(12*12))*0.036/(1-(1+0.036/12)**(12*12))/12

11.974611616707898

Problem 4

a)

def fun(n):
    if n == 0:
        return 1
    else:
        return 2*fun(n-1) + 3

fun(16)

262141

b)

def stairs(n):
    if n == 1:
        return 1
    elif n == 2:
        return 1
    elif n == 3:
        return 2
    elif n == 4:
        return 4
    else:
        return stairs(n-4)+stairs(n-3)+stairs(n-1)

stairs(18)

3025

Problem 5

def bisection(a,b,f,err):
    c = (a+b)/2
    while c-a > err:
        if f(c) == 0:
            return n
        elif f(c)*f(a) > 0:
            a = c
        else:
            b = c
        c = (a+b)/2
    return c

a)

def p(x):
    return x**3-5*x+5

bisection(-3,-2,p,0.01)

-2.6328125

b)

import math

def gPrime(x):
    return math.exp(x)-1/x

bisection(0.25,3,gPrime,0.01)

0.56689453125

Problem 6

def sevenCounter(arr):
    if len(arr) == 1:
        if arr[0] == 7:
            return 1
        else:
            return 0
    else:
        if arr[0] == 7:
            return 1 + sevenCounter(arr[1:])
        else:
            return sevenCounter(arr[1:])