The value of b is [tex]1 \cdot02[/tex].
What is compound interest?
Compound interest is when you earn interest on both the money you have saved and the interest you earn.
Formula for compound interest is
[tex]A= P(1+\frac{r}{100})^n[/tex] ...................(1)
where, A = total amount( principal + interest )
r = rate of interest in compound interest
n = number of years
Given,
For [tex]n=1[/tex]
Principal amount [tex]p=\$ 1000[/tex]
Total amount [tex]A=\$ 1020[/tex]
For [tex]n=2[/tex]
Principal amount [tex]p=\$ 1000[/tex]
Total amount [tex]A=\$ 1040[/tex]
This scenario can be represented by an exponential function of the form of [tex]f(x)=1000(b)^x[/tex]
Comparing the above function with equation (1), we get
[tex]A=f(x)\\P=1000\\b=(1+\frac{r}{100})[/tex]
For 1st year
[tex]f(x)=1000(b)^1\\\Rightarrow 1020=1000(b)\\\Rightarrow b=\frac{1020}{1000}\\\Rightarrow b= \frac{102}{100}\\\Rightarrow b= 1\cdot02[/tex]
now, check the amount for 2nd year
[tex]f(x)=1000 \times (1 \cdot01}^2\\\Rightarrow f(x)=1000 \times \frac{102}{100}\times \frac{102}{100}\\\Rightarrow f(x)=1040[/tex]
Hence, the value of b is [tex]1 \cdot02[/tex] .
To learn more about compound interest from the given link
https://brainly.com/question/24924853
#SPJ4
