Ben makes a deposit of $1,200 into a savings account. the bank calculates simple interest annually at a rate of 6%. interest is added every year on the anniversary of the initial deposit. how many years must ben wait before his investment exceeds $1,500? give your answer in years.

Ben must wait more than 4.2 years

Step-by-step explanation:

step 1

we know that

The simple interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

substitute the values

Solve for t

Divide by 1,200 both sides

Subtract 1 both sides

Divide by 0.06 both sides

therefore

Ben must wait more than 4.2 years

i need points

step-by-step explanation:

sorry bubs

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places