Answer:
Step-by-step explanation:
[tex]1036.66=1000e^{2r}\\ \\ r=(ln(1.03666))/2\\ \\ r=0.018\\ \\ b(x)=1000e^{(0.018x)}\\ \\ b(10)=1000e^{0.18}=\$ 1197.22[/tex]
The equation for the best-fitting exponential function is A = 1000 (1.01816)ˣ. And the amount of money in the account after 10 years will be $ 1197.18.
Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
You open a savings account and deposit $1,000.
After 1 year of earning continuously compounded interest.
Your balance is $1.018.16. After 2 years, the balance is $1.036.66.
Assuming you make no deposits or withdrawals.
Then the equation for the best-fitting exponential function represents the balance of the account after x years will be
A = 1000(1 + r/100)ˣ
After one year, the amount will be 1018.16 dollars. Then the value of r will be
1018.16 = 1000 (1 + r/100)¹
1 + r/100 = 1.01816
r/100 = 0.01816
r = 1.816%
Then the equation will be
A = 1000 (1.01816)ˣ
Then the amount of money in the account after 10 years will be
A = 1000 (1.01816)¹⁰
A = 1000 x 1.19718
A = $ 1197.18
More about the compound interest link is given below.
https://brainly.com/question/25857212
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