Answer :
To find out the balance owed after 46.5 months if the growth is exponential, we start with the exponential growth formula:
[tex]\[ f(x) = 800(1 + 0.096)^x \][/tex]
In this formula:
- [tex]\( 800 \)[/tex] is the initial balance on the credit card.
- [tex]\( 0.096 \)[/tex] is the growth rate per month.
- [tex]\( x \)[/tex] is the number of months, which in this case is 46.5.
To find the balance after 46.5 months:
1. Insert the values into the formula:
[tex]\[ f(46.5) = 800 \times (1 + 0.096)^{46.5} \][/tex]
2. Calculate the expression inside the parentheses:
[tex]\[ 1 + 0.096 = 1.096 \][/tex]
3. Raise [tex]\( 1.096 \)[/tex] to the power of 46.5:
[tex]\[ (1.096)^{46.5} \][/tex]
4. Multiply the result by 800 to get the final balance.
After performing these steps, the balance is found to be:
[tex]\[ 56791.16 \][/tex]
Hence, after 46.5 months, the balance on the credit card would be approximately \$56,791.16, rounded to the nearest cent.
[tex]\[ f(x) = 800(1 + 0.096)^x \][/tex]
In this formula:
- [tex]\( 800 \)[/tex] is the initial balance on the credit card.
- [tex]\( 0.096 \)[/tex] is the growth rate per month.
- [tex]\( x \)[/tex] is the number of months, which in this case is 46.5.
To find the balance after 46.5 months:
1. Insert the values into the formula:
[tex]\[ f(46.5) = 800 \times (1 + 0.096)^{46.5} \][/tex]
2. Calculate the expression inside the parentheses:
[tex]\[ 1 + 0.096 = 1.096 \][/tex]
3. Raise [tex]\( 1.096 \)[/tex] to the power of 46.5:
[tex]\[ (1.096)^{46.5} \][/tex]
4. Multiply the result by 800 to get the final balance.
After performing these steps, the balance is found to be:
[tex]\[ 56791.16 \][/tex]
Hence, after 46.5 months, the balance on the credit card would be approximately \$56,791.16, rounded to the nearest cent.