Answer :
Answer: a) [tex]b= p(1 + r)^1[/tex] b) [tex]c= p(1 + r)^n[/tex] c) [tex]d= p(1 + r)^m[/tex] d) [tex]b^n=c[/tex]
Step-by-step explanation:
Since f is an exponential function.
So, it is expressed as
[tex]f = p(1 + r)^[/tex]
Here f is the present value
p is the initial value
r is the rate of growth per time period
t is the time period.
(a) b represents the 1-unit growth factor for f.
[tex]b= p(1 + r)^1[/tex]
(b) c represents the n n-unit growth factor for f.
[tex]c= p(1 + r)^n[/tex]
(c) d represents the m m-unit growth factor for f.
[tex]d= p(1 + r)^m[/tex]
Write a formula that expresses c in terms of b.
Since
[tex]b=p(1+r)^1\\\\So,\\\\b=p(1+r)^{n\times \frac{1}{n}}\\\\b=(p(1+r)^n)^{\frac{1}{n}}\\\\b=c^{\frac{1}{n}}\\\\b^n=c[/tex]
Hence, a) [tex]b= p(1 + r)^1[/tex] b) [tex]c= p(1 + r)^n[/tex] c) [tex]d= p(1 + r)^m[/tex] d) [tex]b^n=c[/tex]