$4^{x} + 1 = 64 \\4^{x} = 63 \\ln(4^{x}) = ln(63) \\xln(4) = ln(63) \\x = \frac{ln(63)}{ln(4)}$

$(\frac{ln(63)}{ln(4)})^{4} = 79.78006702$

The value of x⁴ is equal to 79.8006702

7 0

3 years ago

Micah needs $18,500 to purchase a boat. How much money will he need to invest today in a savings account earning 3.2% interest,

charle [14.2K]

We have that every quarter, he will get an 0.8% interest rate. We also have that there will be 14*4=56 periods of repayment. We have that by the formula, if there are n periods and x% is the interest rate, the capital is multiplied by (100+x%)^n.
Suppose Micah invests x money. Then, we have that after 14 years, the capital available will be C= $x*(1.008)^{56}=x*1.562$ . We have that C=18500$ and hence that 18500=x*1.562. Thus, solving for x we have that x=11841$.
Micah will need to invest only 11841$ in order to pay for his boat; this shows the importance of saving since he earns a lot of money, around 7k $.

6 0

3 years ago