(a) At a simple interest rate of 12% per year, determine how long it will take $5000 to increase to twice as much. (b) Compare the time it will take to double if the rate is 20% per year simple interest.
Explanation:
10000=5000(1.12^x)
2=1.12^x
(log_1.12)(2)=x
x= about 6.1163
10000=5000(1.2^x)
2=1.2^x
(log_1.2)(2)=x
x= about 3.8019
compare them by saying like 20% will be 6.12/3.8 times faster
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. Ex = 6 − 5x, (0, 1) The equation ex = 6 − 5x is equivalent to the equation f(x) = ex − 6 + 5x = 0. F(x) is continuous on the interval [0
Answer:
some part of your question is incomplete
attached below is the complete question
Answer :
F(0) = -5 < 0
F(1) = e - 1 > 0
since the functions : f(0) and f(1) have opposite signs then there is a 'c' whereby F(c) = 0 ( intermediate value theorem fulfilled )
Hence there is a root in the given equation : [tex]e^x = 6 - 5x[/tex]
Explanation:
using Intermediate value Theorem
If F(x) is continuous and f(a) and f(b) have opposite signs then there will be a'c'E (a,b) whereby F(c) = 0
given equation : [tex]e^x = 6 - 5x[/tex] on (0,1)
and F(x) = [tex]e^x - 6 + 5x = 0[/tex]
This shows that the F(x) is continuous on (0,1)
F(0) = [tex]e^0 - 6 + 5(0)[/tex] = -5 which is < 0
F(1) = [tex]e^1 -6 + 5(1)[/tex] = e -1 > 0 and e = 2.7182
since the functions : f(0) and f(1) have opposite signs then there is a 'c' whereby F(c) = 0 ( intermediate value theorem fulfilled )
Hence there is a root in the given equation : [tex]e^x = 6 - 5x[/tex]