Question

Natalie has $5000 and decides to put her money in the bank in an account that has a 10% interest rate that is compounded continuously.
What type of exponential model is Natalie’s situation?
Write the model equation for Natalie’s situation
How much money will Natalie have after 2 years?
How much money will Natalie have after 10 years?

Answer 1

Answer:

Part 1) Is a exponential growth function

Part 2)  $A=5,000(e)^{0.10t}$    or  $A=5,000(1.1052)^{t}$

Part 3) $\ 6,107.01$

Part 4)  $\ 13,591.41$

Step-by-step explanation:

Part 1) What type of exponential model is Natalie’s situation?

What type of exponential model is Natalie’s situation?

we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

$P=\ 5,000\\r=10\%=0.10$  

substitute in the formula above

$A=5,000(e)^{0.10t}$  

Applying property of exponents

$A=5,000(1.1052)^{t}$  

therefore

Is a exponential growth function, because the base is greater than 1

Part 2) Write the model equation for Natalie’s situation

$A=5,000(e)^{0.10t}$    or  $A=5,000(1.1052)^{t}$

see Part 1)

Part 3) How much money will Natalie have after 2 years?

For t=2 years

substitute

$A=5,000(e)^{0.10*2}=\ 6,107.01$

Part 4) How much money will Natalie have after 10 years?

For t=10 years

substitute

$A=5,000(e)^{0.10*10}=\ 13,591.41$